How is the nature of civilization relevant to Shakespeare's Othello?

One of the themes of the play is the nature of what people consider to be civilized. Within the world of the play, Venice represent the "civilized" European world and Othello, as a Moor, is a "barbarian" or outsider.
The first issue you should address in your essay is the historicity of this viewpoint. The play is set in Venice in the sixteenth century. At this period, the Ottoman Empire had conquered Constantinople and was vast and powerful. The Moors (followers of Islam of Arabic or North African descent) were also powerful and possessed a venerable and sophisticated civilization which, unlike the Latin West, had not collapsed into a "Dark Ages" but maintained continuity of knowledge; much of the European Renaissance, in fact, had been due to recovery of ancient learning via contact with the Moors in Spain. Thus, although the play presents Venice as civilized and the Moor as originating outside "civilization," those labels are not historically accurate.
Next, we can also problematize the concept of civilization by looking at the qualities of the characters in the play. Many of the members of Venetian society, despite a veneer of polite manners, are the true moral barbarians, duplicitous, longing for material wealth and position, and morally corrupt. Iago, a noble Venetian, is much less honorable than the barbaric Othello. 
Finally, we might look at the military background of the play and argue that both Venice and the Ottoman Empire are in Cyprus for identical reasons of promoting mercantile and territorial advantage. Both great civilizations are shown here as equally rapacious and, in a sense, "uncivilized."

What are the key concepts of Embodied Cognition?

Embodied Cognition is the idea that cognition is controlled by factors in the body beyond just the brain. In other words, the brain affects the body, and the body affects the brain. The central thesis of embodiment is that cognitions are dependent on the physical body and that the body plays a major role in cognition. Embodied Cognition posits that cognitions are not only controlled by internal factors. Other factors that influence our thinking include our perceptions, the motor system, and the body's interaction with the environment. The key concepts in this theory are that cognitions arise from sensorimotor perceptions and that sensorimotor perceptions are part of a larger biological and psychological context. 
Embodied cognition in part arises from the theories of the philosophies of Heidegger, Dewey, and others. Embodied Cognition is part of the fields of psychology, in which it is posited that the motor system affects the choices we make and our decision making. George Lakoff and others have explored the idea of Embodied Cognition in linguistics, and it also has connections to robotics and artificial intelligence.

What is a good topic in the Odyssey to write an eight-page research paper on?

For a research paper, you can try discussing certain themes from The Odyssey. I will discuss two below.1) HospitalityThis is one of the major themes of the story. Some questions to explore:a) Should hospitality be regarded as a reciprocal arrangement?b) If guests abuse their privilege, what recourse does the host have?c) If the host in question is powerless to prevent her quests from taking further unwanted liberties with her person and property, should she resort to violence? If she cannot do so, should another party resort to violence on her behalf?In the story, Odysseus' wife, Penelope, is powerless against the machinations of her suitors. They shamelessly consume food and drink at Odysseus and Penelope's expense, and they also appropriate every luxury in the couple's palace for their own. Here, you can refer to the text to help you provide examples for the suitors' despicable conduct.With Odysseus missing and Telemachus weakened by his fear, Penelope is forced to repress her anger. Instead, she uses her wits to keep her suitors at bay. She resorts to trickery by telling them that she must finish Laertes' shroud before she can marry any of them. Each night, she unravels her work so that the shroud is never completed. For three years, she manages to trick her suitors with her story. Later, when she senses that Odysseus is nearby (in the guise of the beggar), Penelope becomes more confident. She proclaims that she will only marry the suitor who can wield Odysseus' bow successfully.Of course, the beggar (being Odysseus) is the only one who can truly wield his bow. Upon being exposed as Odysseus himself, the long-suffering husband proceeds to slaughter all of Penelope's suitors. Now, the denouement raises interesting questions. The suitors' relatives demand restitution for the deaths. Are their claims valid? Is Halitherses' proclamation that the suitors received their just deserts a good argument? Essentially, we revisit the question of whether hospitality should be a reciprocal arrangement. Your answer to this can be used as a working thesis statement for your essay.2) Loyalty/ Fidelity.Loyalty is a main theme in The Odyssey, and in Penelope's case, loyalty is richly rewarded. In the story, servants who remain loyal are also presented in a positive light. Some questions to consider regarding this theme:1) Does gender play a role in defining loyalty? How does Penelope's loyalty differ from her husband's conception of marital fidelity?Compare and contrast Penelope's sexual fidelity and Odysseus' seemingly gratuitous sexual indulgence while he is away. At the same time, it can be said that Odysseus is loyal in his own way: he overcomes great odds to return home to his wife and son. Is it possible to reconcile the two differing standards of loyalty? 2) How do loyal servants preserve familial integrity? In The Odyssey, Eurykleia is a minor character, but her influential position helps her convince Telemachus to stay with Penelope. When Odysseus returns, she is one of the original few who recognizes him through his disguise. For more information about this, please refer to Book 19.Basically, you can discuss how Homer uses the differing types of loyalty to tell an engaging story and to provide a glimpse into ancient attitudes about love, family, and community.

There are several topics that can be explored in a research paper on The Odyssey.
--The roles of the gods and goddesses
Certainly, there are many instances in which Odysseus cannot achieve what he does without divine intervention. Then, too, Odysseus is often impeded from a successful return by deities such as Calypso, who holds him for years. And, if Athena had not intervened (along with Zeus), Odysseus may have remained with Calypso.
--Odysseus as the model for the tragic hero
Interestingly, it was Aristotle himself who ascribed to Homer the beginnings of Athenian tragedy and comedy. While Achilles and Hector of the Iliad hint at the tragic hero, in the Odyssey, critics contend that the standards of tragedy later developed by Aristotle in his Poetics are demonstrated. 
Thus, using the Poetics as the framework, a paper could develop an analysis of the Odyssey as containing certain elements of tragedy. Clearly, Odysseus is heroic as he is among those who have taken their share of plunder from the Trojans. However, he is the only one who does not return home. And so begins his long journey homeward in which he must struggle against wicked men and interfering deities. Moreover, even when he reaches home, he is met with insult and must conquer enemies there.
In tragedy, Aristotle declared,a) The intention must be "to express true fact under impossible combinations."b) "The plot, then, is the first principle, and, as it were, the soul of tragedy. Character holds the second place."

One interesting paper topic would be Homer's portrayal of father-son relationships, concentrating on the relationship between Telemachus and Odysseus. When the epic starts, Telemachus has never met his father and does not know he's alive, but, with Athena's inspiration, he begins to search for news of his father and matures as a result. The first four books of the epic concentrate on Telemachus's maturation from a daydreaming boy to a more confident young man who is willing to take on the suitors. How does Telemachus come of age, and how does his relationship with his father and their eventual reunion support or complicate his maturation?
Another interesting potential topic is the role of women in Homer's epic. Athena, a goddess, is a strong character who motivates and inspires both Telemachus and Odysseus. Penelope is strong in her own way, though she shows greater use of passivity. They both use deception--Penelope by knitting and unknitting a shroud that she says she must finish before choosing to marry one of the suitors--and Athena through using disguises for herself and for Odysseus. Goddesses such as Calypso model another form of being a woman. What is Homer suggesting is the proper role of a women in Greek society, and what kinds of power do women possess?
The use of deception is another idea for a paper, as the use of deception helps Athena, Penelope, and Odysseus defeat the suitors. Deception has both physical aspects (for example, Athena's use of disguises) and psychological aspects (for example, Odysseus's appearing weak before the suitors), and a paper could examine how characters use deception to defeat more powerful opponents and obstacles.

Moose moves to a new place. Describe at least two positive effects and two negative effects of this change on Moose.

In the novel Al Capone Does My Shirts, the protagonist, Moose, moves with his family to Alcatraz so his father can begin a job as a prison guard.
Moose is in seventh grade and must start a new school, while his sister, Natalie, who is autistic, hopes to get accepted into a special school in San Francisco.
Moose misses his old baseball buddies from his former school and doesn't yet know how he will fit in with his new classmates. The negative effects of the move for Moose are more noticeable at first; his sister is not accepted into the school in San Francisco, so Moose must "babysit" her after school everyday. Moose's mother is a music teacher and Moose's father is busy with his job, so that leaves Moose to take care of her. Since Natalie is autistic, this is a very difficult task.
Moose also becomes acquainted with a classmate named Piper who just happens to be the daughter of the warden of the prison. The enterprising Piper develops a scheme by which she hopes to make extra money from classmates by offering to have their clothes washed by the world-famous Al Capone. Moose has no choice but to help Piper, as he wants to stay in her good graces. Moose is later found guilty by association.
The positive effects of the move to Alcatraz show up a little later. Moose eventually does make friends, especially with Scout, with whom he enjoys playing baseball. And although Moose is still angry with Piper for involving him in the laundry plan, he decides to ask for her help in getting Natalie accepted to the special school in San Francisco. Natalie decides to stick a note in one of the sleeves of Al Capone's shirt. Within days, Moose finds out that Natalie has been accepted to the prestigious school:

Moose finds a note from Capone in the sleeve of one of his convict-washed shirts that simply says: "Done."

Moose learns to appreciate life on Alcatraz and to understand his parents and his sister in deeper ways.
https://www.publishersweekly.com/978-0-399-23861-1

At first, the move to Alcatraz Island seems entirely negative for Moose. He is leaving behind his friends and a regular life on the mainland for a more isolated, and certainly unusual, life on an island. This causes a lot of anxiety as he acclimates to this new existence. Another negative effect, from Moose's point of view, is that he feels imprisoned, so to speak, by his duties watching his autistic sister, Natalie, each day after school while his mother attends to business on the mainland. He misses playing baseball on the one "off" day he has from caring for Natalie, and causes tension between Moose and his best friend, Scout.
As the story progresses, more positive attributes of the move are revealed. For one, Moose gains increasing empathy for Natalie—to the point where, at the end of the story, he apparently enlists the aid of a notorious criminal housed on Alcatraz, Al Capone, to help get Natalie into a promising new school for her condition. Moose also gains insight into human nature, as he deals with a hypocritical warden and her conniving daughter, then indirectly with a pair of prisoners—Capone, and "Number 105," who walks Natalie by the hand one day when Moose leaves her unattended.
The unique situation stirs a lot of personal growth for Moose. He wrestles with morality, in both how to deal with a laundry scheme, and in urging his mother at the end to stop being deceptive about Natalie's age.

Moose is not particularly thrilled to move to Alcatraz Island because he shares the island with notorious convicts; therefore, a negative effect of the move is that he feels jumpy. In fact, he plans to sleep in his clothes so that he does not meet a convict while wearing his pajamas. Another negative effect of the move is that he has to move away from his old friends, which includes his best friend, Pete.
A positive result of his move is that his sister, Natalie, can attend the Esther P. Marinoff School, which his family hopes will help her (as she has autism). Moose wants his sister to get help, though he will miss her, so this is a positive effect of the move. In addition, moving is positive because Moose's dad has a solid job as an electrician at the prison. When Natalie leaves the island to attend school, Moose has more time to spend with his father.

Why and how and to what extent was the First World War a global war?

WWI was a global war in the sense that every inhabited continent had troops who participated in the conflict.  British, French, and German colonial subjects all fought in the war, many of whom were drafted to serve in European trenches.  There were a few battles in East Africa and in the Pacific islands--Japan used WWI as an excuse to take over German-held colonies.  The Atlantic Ocean and Mediterranean Sea became battle zones, as German U-boats waged war against Allied shipping.  Manufactured goods and foodstuffs came from the Americas in order to fuel the Allied war effort.  The Middle East erupted into conflict as Britain and Germany both tried to control Muslims in the area to either fight against Allied areas or to overthrow the Ottoman Empire--ultimately, British efforts in the region were successful in forcing the Ottoman Empire out of the war.  The conflict was even taken to the United States in the form of German spies and saboteurs; German agents managed to destroy the Black Tom munitions plant at Jersey City.  
The end of the war was also an international affair.  British and French colonies wanted their own independence through Wilson's promise of self-government for all people, but were turned down.  The interwar period was important for nationalist movements in the Middle East, Asia, and Africa.  WWI also changed Europe as well, with the formation of Poland and the Baltic countries from land taken from the Soviet Union and Germany.  The Austro-Hungarian Empire split and the Versailles treaty makers created the nation of Yugoslavia in order to placate the nationalist movements there which started the war.  

Now that the Revolutionary War had been fought, how did the framers and revolutionaries go about forging and forming a national republic/new nation between 1776 and 1789?

As soon as the colonies agreed to declare independence, each set about establishing a state government. The constitutions that were written and established in the various states varied in form—Pennsylvania's for example, was quite democratic—but they generally established governments based on the principles of separation of powers and representation, a set of beliefs sometimes called republicanism. These governments struggled with fiscal issues in particular, as the Revolutionary War placed a tremendous strain on scarce resources. The states also struggled to agree on a national government, establishing a loose organization known as the Articles of Confederation, which did not go into effect until 1781, when the war was all but over. This government reflected the fear, shared by many Americans, of excessive centralized power. The congress it created was very weak, lacking the power to tax, and there was no centralized executive power. Fiscal crises at the state level led to popular unrest, and many of the Founders feared that state governments were too democratic, and the national government too weak, to deal with the issues confronting the nation. The Constitutional Convention of 1787 was intended to address these issues, and it established a national republic that curtailed the powers of the states while allowing for limited participation in government by the people. Mainly, it sought to deal with the challenges of the postwar era by placing expansive powers in the hands of the central government. It was the founding document for the new nation that was forged out of the chaos of the post-Revolutionary War period.
https://www.archives.gov/founding-docs

What is the duality between England and France in A Tale of Two Cities by Charles Dickens?

In A Tale of Two Cities by Charles Dickens, Dickens outlines the duality and contrasts between England and France at the time. More specifically, he outlines the duality between Paris and London. The title, in fact, hints that Dickens will present the story of two cities. He establishes the parallelism and duality between the two cities at the very beginning of the novel:

It was the best of times,it was the worst of times,it was the age of wisdom,it was the age of foolishness...

If it was the best of times, how could it simultaneously be the worst of times? We know that Dickens is writing about these two cities at the time of the French Revolution. It was the best of times in London perhaps, but it was the worst of times in Paris, where chaos reigned. Dickens writes, “Along the Paris streets, the death-carts rumble, hollow and harsh.”
Describing the respective monarchies, Dickens sets up the two cities as near mirror images of one another:

There were a king with a large jaw and a queen with a plain face, on the throne of England; there were a king with a large jaw and a queen with a fair face, on the throne of France. In both countries it was clearer than crystal to the lords of the State preserves of loaves and fishes, that things in general were settled for ever.

Dickens also writes, “we had everything before us, we had nothing before us.” If you lived in London and came from a certain economic background, you had everything before you. However, if you lived in Paris and came from that same economic background, you had nothing before you but the prospect of prison or death.
While London is contrasted with the chaos of Paris, the prisons in both cities seem equally difficult to endure. Darnay and Doctor Manette discuss the Tower (of London). Darnay was imprisoned there, he recalls “with a smile, though reddening a little angrily.” Similarly, Doctor Manette was imprisoned in the Bastille, and it drove him mad for a while.

There seem to be dualities and similarities between England and France. Both countries have monarchs and landed aristocracy, yet a number of differences set them apart. London stands for calm and order. Even though the poor in London suffer disproportionately to the rich, there is still due process of law, and even cruel sentences are not capricious. France, by contrast, stands for chaos. The same inequality between rich and poor exists, but the French aristocracy is not restrained from doing whatever comes into their minds. When the marquis runs over and kills the peasant child, the people of the village have no recourse.
Two revolutions are mentioned in this story, and they both illustrate the difference between England and France. The American Revolution does not affect life in London. Aside from his comment that "messages...had lately come to the English Crown and people from a congress of British subjects in America which have proved...important to the human race," Dickens does not speak of the American Revolution directly again. That struggle was initially carried out after orderly petitions to the Crown by people accustomed to an orderly way of life. The French Revolution was a result of centuries of oppression. There was little planning for what would come after a successful overthrow. The revolution convulsed Paris with mob violence and gruesome public executions. It took the reign of Napoleon to finally bring a stable government to France.
https://www.charlesdickensinfo.com/novels/tale-two-cities/

The title of the novel signals the importance of two cities—London and Paris—during the French Revolution in the late eighteenth century. London represents calm and order in contrast to the overflow of violence and mayhem in revolutionary Paris. 
The Manettes's home in London most fully represents safety and happiness. There Dickens illustrates a major theme across his writing: that good, kind people treating others well are the surest basis of a humane society.
In Paris, on the other hand, tensions have long been simmering due to wealth inequality and the brutal exploitation of the poor by the rich. Dickens does not shy away from condemning the cruelty of the wealthy aristocrats. The marquis becomes a caricature of cruelty in his determination to keep peasants down and in his indifference at running over and killing a peasant child. Additionally, Dickens deplores the mob violence and bloodshed that erupts into revolution, including the barbarity of murdering the wealthy in their beds, and the seemingly endless working of guillotine.
The novel is also a cautionary tale for the English: unless the privileged in London change their hearts and actions, there is no guarantee similar violence will not erupt there.

The duality of Paris (the capital city of France) and London (the capital city of England), comparing and contrasting the nature of the two cities, presents a foundational theme of the novel—order versus chaos. London is portrayed as a place of safety and peace. Its society is well-ordered and purposeful, personified in the character of Jarvis Lorry, the banker. There are rules to be followed, regardless of personal choice. Although the novel is set during the American Revolution, the war does not affect the life of the average person in London. All life goes on as usual, with the surface of society seeming to be unruffled.
In Paris, chaos is erupting on all levels. The nobility is desperately sheltering itself from the troubles of the poor, while the poor are beginning to simmer, ready to boil over. There is no peace, even though the beginning of the story depicts the people as living in their misery with no outward confrontation. This is especially personified in the characters of Monsieur and Madame Defarge as they talk of the change that is sure to come when the time is right. The breaking point is finally reached and the revolution breaks out, destroying poor and rich alike. The chaos leaks into London, but only in the sense of the nobility seeking shelter and protection. Charles Darnay and the others must willingly enter the chaos of the French Revolution, breaking through the symbolic barrier of peace separating the two cities.

What point of view is represented in Burr by Gore Vidal?

"Burr" is an iconic novel by author Gore Vidal that focuses on the true history of the Founding Fathers of the United States of America. The story is told from the point of view of a young Charles Schuyler, a twenty-five-year-old man who served as a law clerk in Aaron Burr's office. Burr was the third Vice President of the United States, serving alongside President Thomas Jefferson during his first term. The decision to tell the story of "Burr" from young Schuyler's point of view is an interesting one, as Vidal uses Schuyler's youthful naïveté and optimism to shine a light on the more scandalous aspects of Burr's service.
Through Schuyler's eyes, the reader is able to see Burr as he really was, a figure surrounded by more controversy and moral dilemmas than his relatively sanitized portrayal in the average history textbook would suggest. The story begins in 1833 and tells of Schuyler's exploits as Burr's clerk, and ends four years after the former Vice President's death. Burr's perspective is made all the more intriguing by the fact that he hopes to abandon his life of politics to become a professional writer.
Schuyler is at first enamored with the sophisticated politician and envies his worldly qualities. As "Burr" continues, his naïveté is shattered and be begins to realize that the man does not fully live up to his public reputation. Through a variety of political schemes and vices, Schuyler is indoctrinated into the world of political intrigue and the reader experiences it all through his first person perspective.
The use of first person point of view allows Vidal to inject a significant amount of humor and personality into the narration. Schuyler's voice is witty and full of enthusiasm, making "Burr" an engaging read from the first page. Observations about the other characters, such as "Shortly before midnight, July 1, 1883, Colonel Aaron Burr, aged seventy-seven, married Eliza Jumel, born Bowen fifty-eight years ago (more likely sixty-five, but remember: she is prone to litigation!)" offer humorous insights into the various ways in which their personal lives contradict the public images they project.
"Burr" is an excellent example of the use of first person point of view that lends personality to a narrative that might otherwise feel dry or forced if told from an impersonal third person point of view. Having Burr's story told from someone close to him also allows Vidal to delve into his exploits with greater honesty and sympathy than if he had written it from Burr's point of view or that of an omniscient narrator.

In Part One of "The Dialogues on Natural Religion" by David Hume, Cleanthes accuses Philo of attempting to erect religious faith on philosophical skepticism. What does Cleanthes mean by doing this?

In Part One, Cleanthes means to expose what he believes are flaws in philosophical skepticism. Philosophical skepticism is the belief that human reason is fallible and therefore cannot be used as a benchmark to determine the reality of established truths. Philosophical skeptics doubt whether they can ever obtain enough convincing evidence (or justification) to support popular assumptions.
Philo maintains that human reason alone is insufficient to determine the validity of religious claims:

Let us become thoroughly sensible of the weakness, blindness, and narrow limits of human reason: Let us duly consider its uncertainty and endless contrarieties, even in subjects of common life and practice...When these topics are displayed in their full light...who can retain such confidence in this frail faculty of reason as to pay any regard to its determinations in points so sublime, so abstruse, so remote from common life and experience?

Philo claims that it's fine to rely on "common sense and experience" when it comes to mundane matters such as "trade, or morals, or politics, or criticism." After all, we're dealing with tangible concepts here. However, he argues that human reason can't accurately determine how "the creation and formation of the universe" really came about. Philo questions how we can prove with any degree of certainty "the existence and properties of spirits; the powers and operations of one universal Spirit existing without beginning and without end; omnipotent, omniscient, immutable, infinite, and incomprehensible..."
It should be noted that Philo isn't proposing absolute skepticism here (absolute skepticism is the belief that truth cannot be determined). However, he is arguing that, in matters of theology, we humans have no concrete way of determining the validity of absolute truths.
For his part, Cleanthes argues that faith is essential when it comes to matters of theology. He aims to point out the hypocrisy in Philo's position of philosophical skepticism, especially in this area. Cleanthes puts forth the argument that Philo accepts scientific truths that are speculative in nature (for the time, at least). So, he questions why Philo cannot transfer this openness to matters of theology. Here are his words:

In reality, would not a man be ridiculous, who pretended to reject NEWTON's explication of the wonderful phenomenon of the rainbow, because that explication gives a minute anatomy of the rays of light; a subject, forsooth, too refined for human comprehension? And what would you say to one, who, having nothing particular to object to the arguments of COPERNICUS and GALILEO for the motion of the earth, should withhold his assent, on that general principle, that these subjects were too magnificent and remote to be explained by the narrow and fallacious reason of mankind?

So, in questioning Philo's attempt to erect religious faith on philosophical skepticism, Cleanthes aims to expose the dangers of a "brutish and ignorant skepticism" that will "reject every principle which requires elaborate reasoning to prove and establish it." Cleanthes contends that such skepticism is "fatal to knowledge." He invites Philo to reconsider his views.
https://plato.stanford.edu/entries/skepticism/

How would you write a two-page, informal response to Tennyson's poem "Oenone," focusing on the ways in which the elemental and biological imagery of the poem mirrors/echoes the mood of Oenone himself?

As the poem opens, Oenone is sad and heartbroken that Paris, her husband, has left her for Helen. The nature around her reflects her depression by falling silent and drooping, just as she is doing. The imagery is deathlike: the words "quiet" and "silent" reflect the stillness of a corpse, the word "shadow," which can mean ghost or spirit, is repeated twice, and the word "dead" describes the winds. Finally, the flower "droops" as if it is as depressed as Oenone:

For now the noonday quiet holds the hill: / The grasshopper is silent in the grass: / The lizard, with his shadow on the stone, / Rests like a shadow, and the winds are dead. / The purple flower droops[...].

As the poem proceeds, Oenone recalls trying to compete for Paris's love. She pictures her love for him as like "the evening star" and also alludes to herself as a natural creature, a fawn, with a "playful tail." Here, in contrast to the first stanza, she is active, emotional, and full of energy. She compares her love of Paris to

quick-falling dew / Of fruitful kisses, thick as Autumn rains / Flash in the pools of whirling Simois!

Words like "quick," "thick," "flash," and "whirling," as well as the exclamation point, show her to be warm and active when she is remembering her love for Paris and his love for her. She likens herself to parts of nature that are fast-moving: the dew and the autumn rains that "flash" in whirling pools. She compares herself in her hot-blooded embrace with Paris to water swirling in motion. This is a sharp contrast to the dead and drooping nature all around her that she perceives after Paris has left her.
But as she returns to her grief, Oenone again speaks of the nature surrounding her in terms of deathlike imagery. She is, like her lost beloved Paris, a person who feels intense emotions. The beloved hills and woods, which she once enjoyed with Paris, she now describes as cut down:

they cut away my tallest pines,
My tall dark pines, that plumed the craggy ledge
High over the blue gorge.

Now, she experiences "ruin'd folds" and "fragments," as well as "dry thickets." Where once everything was "loud" and beautiful, Oenone perceives it now as somber and silent


Dead sounds at night come from the inmost hills,
Like footsteps upon wool.

Finally, the last stanza nature reflects her anger at Paris's betrayal. Nature becomes fire, a symbol of rage. Oenone states that


wheresoe'er I am by night and day,
All earth and air seem only burning fire.

She moves in the end from depression and grief to rage, pictured as a natural world of earth and air that seems to her now to be "only" fire.

What were Emerson’s attitudes toward law, the family, and education?

In "Self-Reliance," Ralph Waldo Emerson posits that man is sovereign and that no law can bind him except the law of that man's own being. Specifically, Emerson rejects even religious doctrines of conformity in policing the actions of the individual. He writes,

No law can be sacred to me but that of my nature. Good and bad are but names very readily transferable to that or this; the only right is what is after my constitution, the only wrong what is against it.

In his family relations, Emerson called for a kind of stoicism that would allow the continuity of community while maintaining the intellectual independence of the individual. Importantly, he does not seek physical and emotional isolation, only intellectual and spiritual independence. He writes,

I will have no covenants but proximities. I shall endeavour to nourish my parents, to support my family, to be the chaste husband of one wife,—but these relations I must fill after a new and unprecedented way. I appeal from your customs. I must be myself. I cannot break myself any longer for you, or you. If you can love me for what I am, we shall be the happier. If you cannot, I will still seek to deserve that you should.

Emerson rejected what he called the Doric and Gothic models of education, instead advocating for learning through experience, immersion, and interaction with the greater world. He went on to reject the idea of following past paths of success, instead focusing on investigating and developing new avenues and ideas.
http://americainclass.org/individualism-in-ralph-waldo-emersons-self-reliance/

https://archive.vcu.edu/english/engweb/transcendentalism/authors/emerson/essays/selfreliance.html

Emerson's chief theme is that people should follow their hearts and not social conventions. To mindlessly do what your family or society expects of you is the path to misery. This does not mean Emerson believed in abandoning one's family to destitution or disrespecting one's parents, but he did not believe an individual should strive to mold their life according to familial wishes which run contrary to their own nature. As Emerson says of familial obligation in "Self-Reliance," "I shall endeavour to nourish my parents, to support my family, to be the chaste husband of one wife,—but these relations I must fill after a new and unprecedented way." He believes much the same with religious laws: if an individual disagrees with certain doctrines, it is their right.
As for education, Emerson believes students should not try to imitate the great people of the past or accept ideas only because those of the past thought them to be right. Emerson's famous claim "imitation is suicide" relates to this line of thinking. If one only ever copies what others have believed, then they are killing their true self, their own potential as an original thinker.
The binding connection between Emerson's views on family, the law, and education is the belief that every person is unique and lives their best life when they embrace that uniqueness to forge their own path through life.

Emerson thought respect for the law, family, and education was far less important than the need to follow one's inner guide in making life decisions.
"No law can be sacred to me but that of my nature," he writes in response to people who use religious "laws" and rules to suggest people might be guided by the Devil when they reject the counsel of tradition, family, and university education.
Emerson perceives family and education as stumbling blocks keeping too many individuals from finding their God-given destiny. He warns young people embarking on life that they will find no genuine peace and happiness as long as they are following their family's ideas and not their own. He advises his audience to reject book learning, which relies on traditions of the past. Instead, one should go out and experience life directly.
For society to flourish, Emerson argues, everyone must follow the dictates of his or her own heart. "Trust thyself," he says, and eventually everyone around you will respect you and trust you too.

What are the ways that ecological theory supports culturally sensitive work with Hispanic children and families?

On the most basic level, ecological theory concerns how individuals interact or adapt to their environment.
Thus, the ecological approach to social work among Hispanic families centers on acculturation strategies. Acculturation (as related to Hispanic families) refers to how immigrants assimilate or adapt to a culturally foreign environment. Ecological theory supports culturally sensitive work with Hispanic children and families by focusing on solutions within an ecosystem. In ecological or ecosystem theory, the ecosystem is a multi-connected network or matrix that consists of individuals, families, groups, and communities.
Bronfenbrenner (father of the ecological systems theory) hypothesized that the ecological or ecosystems framework allows social workers to study how interrelated systems within an ecosystem contribute to social dysfunction. Thus, analyzing the psycho-social factors that affect the individual allows social workers to find effective solutions to acculturation issues. The ecological/ecosystem approach allows social workers to focus on five main ecosystems that may affect any one immigrant: the microsystem, mesosystem, exosystem, macrosystem, and chronosystem.
The microsystem consists of the immigrant's closest relationships (parents, friends, teachers, caregivers, etc). The esosystem comprises the interaction between the different microsystems in an immigrant's life. For example, a Hispanic child may have supportive parents who attend PTA conferences. Here, the child's microsystems (parents and teachers) engage to provide the support he/she needs to thrive in a foreign environment. 
Meanwhile, the exosystem is not directly connected to the immigrant. It may consist of the child immigrant's parents' employers or members of the larger community. The macrosystem consists of the social, religious, and political systems that influenced the immigrant prior to his/her arrival on foreign soil. Last, but not least, the chronosystem involves changes in the immigrant's life, such as divorces, job transitions, or other types of social upheaval. 
So, ecological theory supports culturally sensitive work with Hispanic children and families by focusing on solutions that incorporate the interrelation between these five systems. Let's take the example of Hispanic elders who must rely on US-oriented caregivers. Many Hispanic elders experience difficulty in reconciling the virtues and values of their native culture with that of the foreign culture they encounter. To be efficient caregivers, nursing and medical staff must communicate an appreciation for the Hispanic patient's culture and values as well as acknowledge the validity of their perspective. Thus, attentive care at the microsystem level can lessen the development of mood disorders such as depression or anxiety among Hispanic elders.
Attention to stress-contributing factors at the exosystem or chronosystem levels is also important. Social workers who use the ecological approach understand the need to address the psycho-social factors that contribute to high poverty levels among Hispanic immigrants. Even though Hispanic immigrants often harbor strong work ethics, the lack of education prevents many from realizing the American Dream. An ecological approach would include on-the-job training, English proficiency classes, and GED classes. It may also include cultural awareness classes, where Hispanic children and families learn to appreciate and understand American culture.
At the exosystem level, many states require those on welfare to fulfill specific work requirements. Because Hispanic families often have low levels of English proficiency, they continue to live subsistence lives. An ecological approach would factor in these language challenges in formulating effective solutions to poverty issues. For example, state agencies may hire and assign Spanish-speaking social workers to work with Hispanic families. Ideally, these workers will have a knowledge of and an appreciation for Hispanic culture. Such workers can facilitate culturally sensitive discussions about the need for English-language proficiency classes, on-the-job training, high school diplomas, college educations, etc. 
For more, please refer to the links below. 

Precalculus, Chapter 1, Review Exercises, Section Review Exercises, Problem 10

Find the intercepts of the equation $y = 5x$ and test for symmetry with respect to the $x$-axis, the $y$-axis and the origin.

$x$-intercepts


$
\begin{equation}
\begin{aligned}

y =& 5x
&& \text{Given equation}
\\
0 =& 5x
&& \text{To find the $x$-intercept, we let $y = 0$ and solve for $x$}
\\
\frac{0}{5} =& \frac{5x}{5}
&&
\\
x =& 0
&&

\end{aligned}
\end{equation}
$


The $x$-intercept is $(0,0)$

$y$-intercepts


$
\begin{equation}
\begin{aligned}

y =& 5x
&& \text{Given equation}
\\
y =& 5(0)
&& \text{To find the $y$-intercept, we let $x = 0$ and solve for $y$}
\\
y =& 0
&&

\end{aligned}
\end{equation}
$


The $y$-intercept is $(0,0)$

Test for symmetry

$x$-axis


$
\begin{equation}
\begin{aligned}

y =& 5x
&& \text{Given equation}
\\
-y =& 5x
&& \text{To test for $x$-axis symmetry, replace $y$ by $-y$ and see if the equation is still the same}

\end{aligned}
\end{equation}
$


The equation changes so the equation is not symmetric to $x$-axis.

$y$-axis


$
\begin{equation}
\begin{aligned}

y =& 5x
&& \text{Given equation}
\\
y =& 5(-x)
&& \text{To test for $y$-axis symmetry, replace$ x$ by $-x$ and see if the equation is still the same}
\\
y =& -5x
&&

\end{aligned}
\end{equation}
$


The equation changes so the equation is not symmetric to $y$-axis.

Origin


$
\begin{equation}
\begin{aligned}

y =& 5x
&& \text{Given equation}
\\
-y =& 5(-x)
&& \text{To test for origin symmetry, replace both $x$ by $-x$ and y by $-y$ and see if the equation is still the same}
\\
-y =& -5x
&&
\\
y =& 5x
&&

\end{aligned}
\end{equation}
$


The equation is still the same so it is symmetric to the origin.

y = ln|sec(x) + tan(x)| Find the derivative of the function.

y=ln|secx+tanx|
To take the derivative of this function, use the formula:
(ln u)' = 1/u* u'
Applying this formula, y' will be:
y' = 1/(secx+tanx) * (secx+tanx)'
To get the derivative of the inner function, use the formulas:
(sec theta)'= sec theta tan theta
(tan theta)' =sec^2 theta
So y' will become:
y' = 1/(secx +tanx) * (secxtanx+sec^2x)
Simplifying it, the derivative will be:
y'=(secxtanx+sec^2x)/(secx+tanx)
y'=(secx(tanx+secx))/(secx + tanx)
y'=(secx(secx+tanx))/(secx+tanx)
y'=secx
Therefore, the derivative of the given function is y' =secx .

How is eating food a physical change?

Actually, eating the food involves both physical and chemical changes. The chewing of food is a physical change, while the mixing of saliva with food triggers chemical reactions and is a chemical change.
A physical change may involve a change in the size, shape or state of a substance; however, its chemical composition stays the same. Chemical change, on the other hand, involves a change in the substance's chemical composition.
When we "eat" the food, we start by chewing it in our mouth. This action causes the food to break down into smaller portions, each of which is still food. In other words, although the size of the food changes, its chemical composition stays the same. This is the part of eating that represents a physical change.
Once the food mixes with the saliva in our mouth, chemical reactions start taking place in the food, leading to its breakdown and changes in its chemical composition. An evidence of the chemical changes is the taste that we feel when we eat something sweet or sour, etc.
Hope this helps. 
 
 

What does Jefferson do to prove his point in the Declaration of Independence?

Jefferson meant in writing The Declaration of Independence to justify the war the colonists were waging to free themselves from British rule. His chief audience included fellow colonists who, whatever their grievances against the British, were uncertain about breaking away from Britain entirely.
Jefferson, therefore, tried to convince his fellow colonists and if possible, the British, of the merit of the revolutionary cause, primarily by piling up multiple examples of British acts of tyranny. This method of persuasion (or rhetorical strategy) is called illustration or exemplification. Using this strategy, an argument becomes convincing if a person can provide enough specific and appropriate examples to back up his or her contention.
Jefferson provides the following illustrations of British tyranny, aiming his ire at King George III, a monarch he accuses, among other things, of the following:

George III has refused to agree to laws that were necessary for the good of the colonists. He has blocked the passage of other necessary laws, trying to trade their passage for the colonists' agreeing to give up representative government. He has made it difficult for legislative bodies to assemble, imprisoned individuals unfairly, interfered with democratic processes, placed a standing army on the continent, and waged war on the colonists. All in all, these accusations paint a portrait of king misusing and abusing democratic institutions to achieve his own ends and undermining legitimate voices in the governing process.

Whether or not this added up to the "absolute Despotism" Jefferson asserted, the cumulative effect of all these examples of George III's malevolence makes a persuasive argument.

Jefferson uses the Declaration of Independence as an opportunity to state his claim that King George, the monarch of Great Britain, is tyrannical and is taking advantage of the colonists for his gain, not for their own benefit. He is attempting first and foremost to make a convincing argument to the people of America, because many still were either uneducated on the subject or believed that George may be acting in their best interests. Additionally, Jefferson was using the document as a way to explain to the British people and other nations that they had due cause for declaring their independence.
His first step in this document is to provide a philosophical framework that George is violating. He states the basic human rights that everyone deserves—life, liberty, and the pursuit of happiness—and goes into details about John Locke's social contract theory, as well as other sociological viewpoints and arguments. This presents a framework for his case. Beyond that, however, Jefferson demonstrates how King George violated their basic rights and went against the framework of a responsible government. Jefferson outlines 27 grievances by the monarch and Parliament to establish a factual basis for what misdeeds had been committed against the Colonists.

Jefferson's "point" in the Declaration of Independence is that the British, through their actions, have broken the social contract that legitimizes government. Therefore, the colonists are justified in declaring their independence and taking their place alongside other nations. In order to defend this argument, he proceeds through a long list of grievances. These are notable because they are directed at King George III rather than Parliament. Some of the most damning charges include the following:

The king had refused to approve laws passed by colonial legislatures.
The king dissolved colonial assemblies.
The king kept standing armies in the colonies, a violation of an age-old English tradition.
The king approved, and attempted to enforce, taxation without representation.

In addition to these charges, Jefferson leveled what would have been read as the final straw for the colonists: The king had encouraged both Native Americans and enslaved African Americans to rise up in revolt against the Revolutionaries. These charges were intended to demonstrate to a "candid world" that the colonies were justified in severing their political ties with Great Britain.

Thomas Jefferson's main point in the Declaration of Independence is that King George is a tyrant and that is reason enough for the colonies to declare their independence from him. Jefferson sets about proving this argument in two ways. He begins the document with a philosophical argument that citizens have the right to a government that respects and protects their natural freedoms and liberties. He borrows a lot of this from the enlightenment philosophers of the 17th and 18th centuries, most notably John Locke. These notions of freedom and self-determination would have been familiar in the intellectual circles of the time. Jefferson contends that if a government will not fulfill its end of this bargain, then the people have a duty to replace it with one that will.
It would not be enough to simply rely on philosophical arguments. Jefferson also provides cases in point as to the tyrannical actions of the English king. He lists twenty-seven grievances against the king that range from imposing taxes without the consent of the people to imprisoning them without the benefit of a proper trial.
Taken all together, Thomas Jefferson lays out a compelling justification of why the 13 colonies were declaring independence from Great Britain and striving to establish a new nation.
https://www.ushistory.org/declaration/document/

Jefferson makes great use of both deductive and inductive reasoning in laying out his argument for independence from Britain.
Deductive arguments are "top-down" in that they begin with the general and move to the specific. Inductive arguments are "bottom-up" and begin with specific observations and move to broader ideas.
Jefferson's general claim (premise) is that King George is a tyrant. Jefferson recites a litany of twenty-seven specific abuses of which the king is guilty. Taken together, these twenty-seven abuses support his claim of the king's tyranny and offer inductive support for his claim.
Other claims that Jefferson makes are more based on philosophical values and are thus less provable, such as his claim of the colonies' right to independence and self-rule. Moreover, Jefferson asserts the claim that all bonds between the colonies and Britain should be dissolved.
Finally, Jefferson claims that when the colonies are free from Britain they, as the independent United States, would be able to act as all independent nations do, another point of deductive logic.

If we accept the notion that a story is a self‐contained whole, then the opening of the story should suggest many of the elements that will be featured throughout. Discuss with reference to Pride and Prejudice or with any two short stories from the course.

The opening lines of a story often hint at the events that will take place later in the text or the themes that will reoccur throughout the story. The opening lines of Pride and Prejudice establish its themes and conflicts right away.
Pride and Prejudice begins with the following famous lines:

It is a truth universally acknowledged, that a single man in possession of a good fortune, must be in want of a wife.
However little known the feelings or views of such a man may be on his first entering a neighbourhood, this truth is so well fixed in the minds of the surrounding families, that he is considered the rightful property of some one or other of their daughters (Austen Chapter 1).

From the outset, the reader can tell that this is going to be a book about finding a suitable marriage. The two young men that most of the action of the book centers around are in fact wealthy, eligible young men. The plot itself revolves around the conflicts that these two men and the Bennet family encounter in love.
The next few lines introduce what will be the conflict for most of the book. When the text says "however little known the feelings or views of such a man may be on his first entering the neighbourhood," this speaks to the fact that Mr. Darcy and Mr. Bingley are indeed new to the neighborhood, and there is a lot of confusion through the majority of the text about exactly what their feelings are. Misinterpretations of their feelings create most of the problems throughout the text. After flirting with Mr. Bingley and then having him suddenly disappear, Jane assumes that Bingley does not actually care for her. Meanwhile, Elizabeth despises Mr. Darcy for most of the novel because she assumes that he is proud, aloof, and unfeeling.
The final part of the quote says that regardless of the designs that the man himself might hold, "this truth is so well fixed in the minds of the surrounding families, that he is considered the rightful property of some one or other of their daughters". This last sentiment is also a major problem in the text. Mrs. Bennet assumes that these wealthy men should, by right, belong to her daughters, and her loud discussion of marriage prospects embarrasses her family and prejudices Mr. Darcy against them.
https://www.gutenberg.org/files/1342/1342-h/1342-h.htm

Should crimes of self-control be treated more harshly than regular crimes? Are they a bigger threat to the system?

Criminologists Hirschi and Gottfredson developed the "General Theory" of self-control, which states that an individual's lack of self-control is the largest factor that determines crime. They believe that self-control increases as a person ages because of biological factors (the development of hormones) and through socialization. Some studies, such as that by Vazsonyi et al. (2007; see the source below) have added validity to the idea that lack of self-control among individuals is a strong predictor of crime. 
Therefore, there is evidence that crimes of self-control are a large threat to the system. Individuals who are insensitive to others' feelings and who are impulsive are generally more prone to commit crimes. According to Hollander-Blumoff (2012; see the sources below), there are several factors that impede self-control, including medical factors present since birth or factors related to one's childhood or rearing. In addition, she writes that the punishment of crimes related to self-control should include rehabilitation:

"Self-control research in psychology also offers a suggestion for both prevention and rehabilitation: if self-control is a resource that can be strengthened over time with practice, perhaps this is a fruitful area for further development in our at-risk populations."

In other words, the best way to deal with crimes involving self-control may not be harsher punishments but prevention of crime by improving people's self-control and rehabilitation. 
Sources
Hollander-Blumoff, Rebecca E., Crime, Punishment, and the Psychology of Self-Control (May 2012). Emory Law Journal, Vol. 61, No. 501, 2012; Washington University in St. Louis Legal Studies Research Paper No. 12-05-22. Available at SSRN: https://ssrn.com/abstract=2080858
Vazsonyi, A. T.; Belliston, L. M. (2007). "The Family → Low Self-Control → Deviance: A Cross-Cultural and Cross-National Test of Self-Control Theory". Criminal Justice and Behavior. 34 (4): 505–530. doi:10.1177/0093854806292299.

In Shakespeare's Macbeth, the main character (Macbeth) receives a prediction about his future in act I, scene 3. Describe this prediction.

At the beginning of act 1, scene 3 of Macbeth, the "Weird Sisters" (the three witches) are gathering to meet Macbeth, which is something they arranged in the first scene of the play:

FIRST WITCH: When shall we three meet again?In thunder, lightning, or in rain?
SECOND WITCH: When the hurlyburly's done;When the battle's lost and won.
THIRD WITCH: That will be ere the set of sun.
FIRST WITCH: Where the place?
SECOND WITCH: Upon the heath.
THIRD WITCH: There to meet with Macbeth. (1.1.1–8)

The witches are already "on the heath" in scene 3 when Macbeth and Banquo show up. The witches have been standing around talking, basically killing time until Macbeth shows up, and one witch shows the others a thumb that she got from a sailor who lost it in a shipwreck; they all seem pretty excited about the sailor's thumb.
When Macbeth and Banquo arrive, they're a little taken aback when they see the witches.

BANQUO: . . . What are theseSo wither'd, and so wild in their attire,That look not like the inhabitants o' the earth . . .You should be women,And yet your beards forbid me to interpretThat you are so.
MACBETH: Speak, if you can. What are you? (1.3.40-49)

The Witches ignore Macbeth's question:

FIRST WITCH: All hail, Macbeth! hail to thee, Thane of Glamis! (1.3.50)

This is not a prediction. Macbeth is already Thane of Glamis.
In Scotland in the eleventh century, the time period in which Macbeth is set, a "Thane" was a nobleman who was permitted by the King to own land in exchange for his military service to the King. (By the way, "Glamis" is correctly pronounced "Glahms," in one syllable.) Macbeth has distinguished himself on the battlefield, and is well known to King Duncan, which gives rise to his ascension to this title.
The second witch speaks up:

SECOND WITCH: All hail, Macbeth! hail to thee, Thane of Cawdor! (1.3.51–52)

Macbeth is confused, since he's not "Thane of Cawdor":

MACBETH: . . . By Sinel's death I know I am Thane of Glamis;But how of Cawdor? The Thane of Cawdor lives,A prosperous gentleman (1.3.74–76)

This looks like a prediction, but it's not.
In scene 2, we learned that the Thane of Cawdor was a traitor to the King in battle, and the King was seriously annoyed about that.

DUNCAN: No more that Thane of Cawdor shall deceiveOur bosom interest. Go pronounce his present death,And with his former title greet Macbeth. (1.3.74–76)

Angus and Ross are going to show up a little later in scene 3 to tell Macbeth that he's now Thane of Cawdor. So even though this is news to Macbeth, it's not a prediction.
Once again, the witches ignore Macbeth's question, and finally get to the point:

THIRD WITCH: All hail, Macbeth, that shalt be King hereafter! (1.3.53)

This is the prediction we're looking for: that Macbeth is going to be King. This might sound like a good thing, except that it sets in motion Macbeth's and Lady Macbeth's extreme ambition, their ruthless, murderous path to the throne, Lady Macbeth's suicide, and Macbeth's death at the hands of Macduff.

Scene 3 of the first act of the play takes place on "a heath near Forres." Three witches are gathered in a thunderstorm, and they anticipate Macbeth's arrival before he first meets them: "Macbeth doth come."
When Macbeth spots the witches, he demands that they speak and tell him who or what they are. Instead of explaining themselves, the witches address him variously as "thane of Glamis," "thane of Cawdor," and Macbeth who "shalt be king hereafter." Banquo, Macbeth's closest friend, asks them why they are saying these things, as they are not all currently true, but the witches simply offer Banquo a mysterious prediction of his own: that he "shalt get kings, though thou be none."
Macbeth demands that the "imperfect speakers" explain further how it is that he can be thane of Cawdor, and indeed how he could ever be king. He knows he is already thane of Glamis "by Sinel's death," but the witches disappear without explaining what they mean by their comments.
However, just as Macbeth and Banquo are discussing the strange prophecies, Angus and Ross arrive to tell Macbeth that he is now indeed thane of Cawdor, just as the witches predicted. This leads Macbeth to wonder whether the final part of their prophecy for him could, indeed, be possible.

In Act 1, Scene 3, the three witches (also known as the Weird Sisters) prophesy that Macbeth will first become the Thane of Cawdor, and then will be crowned King of Scotland. They then claim that, though Banquo himself won't be king, he will be father to a line of kings and, in some sense, will be greater than Macbeth. 
This prediction is important for two reasons. First, it plants the seed in Macbeth's brain that ultimately leads him to murder his way to the throne of Scotland. Second, it alludes to Macbeth's tragic downfall. For example, we learn that, though Macbeth will become king, his reign is doomed to failure, as it is Banquo's line, not Macbeth's, that will last as royalty. As such, through this prediction Shakespeare quickly signals that Macbeth will become king, but that his inevitable failure also looms ominously on the horizon. 

Calculus: Early Transcendentals, Chapter 5, 5.2, Section 5.2, Problem 37

int_-3^0(1+sqrt(9-x^2))dx
Consider the graph of y=f(x)=1+sqrt(9-x^2)
y=1+sqrt(9-x^2)
y-1=sqrt(9-x^2)
(y-1)^2=9-x^2
x^2+(y-1)^2=3^2
This is the equation of circle of radius 3 centred at (0,1)
The integral can be interpreted as the area of a quarter of the said circle and the area of the rectangle whose vertices are (0,0),(0,1),(-3,1) and (-3,0).Plot can be seen in the attached graph.
int_-3^0(1+sqrt(9-x^2))dx
We will use standard integral intsqrt(a^2-x^2)dx=(xsqrt(a^2-x^2))/2+a^2/2arcsin(x/a)+C
=[x+(xsqrt(9-x^2))/2+9/2arcsin(x/3)]_-3^0
=[9/2arcsin(0)]-[-3+9/2arcsin(-1)]
=3-9/2arcsin(-1)
=3-9/2(-pi/2)
=3+(9pi)/4

Oscar Wilde’s The Importance of Being Earnest focuses on surfaces to reveal the problems and hypocrisy of society. The audience is meant to see what the characters do not see. What does the play keep at the surface, and what is the audience is supposed to take away from the commentary about surfaces, in one passage from the play?

One instance of hypocrisy and shallowness in The Importance of Being Earnest is actually one of the first events. In act 1, when Jack (as Ernest) proposes to Gwendolen, their entire exchange is focused on a shallow, surface issue: a name. Jack is only pretending to be named Ernest, and Gwendolen is smitten with the name more than the man. On the surface of this exchange, the only issue that seems to be creating conflict is the simple issue of a name.
Gwendolen actually alludes to the shallowness herself. She states that they live in "an age of ideals" and that her ideal is to "love someone of the name of Ernest." However, her statement about ideals is not meant to be a critique of contemporary life, more a statement with which she has no issue. She even makes a decision as significant as a life partner on basis of one of those ideals, one so shallow that it brought her to accept a proposal on basis of his name. Within the realm of the play, that is the extent of the exchange. However, the audience is able to understand the critiques of society embedded within that exchange. It is the height of silliness to choose a husband based on his name, and while the characters of the play don't seem to find issue with it, the audience is fully aware of the exceedingly arbitrary nature of that reasoning.
This is actually much deeper than it seems at first glance. The shallowness of the entire situation is a pointed jab at the shallowness of society as a whole. It is exaggerated, certainly, but that exaggeration is there to highlight a real issue in the contemporary society. While people may not have literally chosen a spouse based on a name, equally shallow exchanges did occur in Victorian society. For example, many people chose spouses based not on names but on titles, as members of the nobility. So, not only does it point at the shallowness of society, it also reveals the hypocrisy of that same society. While Victorian audience members may have laughed at the situation, they also had to understand that their own society was just as arbitrary as the one portrayed in the play. They would accept or reject a person for reasons as shallow as appearances or titles. The play was ridiculous, but only as ridiculous as the society that it was based on.

Calculus of a Single Variable, Chapter 3, 3.2, Section 3.2, Problem 9

The Rolle's theorem is applicable to the given function, only if the function is continuous and differentiable over the interval, and f(a) = f(b). Since all polynomial functions are continuous and differentiable on R, hence, the given function is continuous and differentiable on interval. Now, you need to check if f(0) = f(3).
f(0) = -0^2 + 3*0= 0
f(3) =-3^2 + 3*3 = 0
Since all the three conditions are valid, you may apply Rolle's theorem:
f'(c)(b-a) = 0
Replacing 3 for b and 0 for a, yields:
f'(c)(3-0) = 0
You need to evaluate f'(c):
f'(c) = (-c^2 + 3c)' => f'(c) = - 2c + 3
Replacing the found values in equation f'(c)(3-0) = 0
3(-2c + 3) = 0 => -6c + 9 = 0 => -6c = -9 => c = 3/2 in (0,3)
Hence, in this case, the Rolle's theorem may be applied for c = 3/2.

How does Anne Wilkinson answer the question "who are we here" in her poem "Winter Sketch, Rockcliffe, Ottawa"?

In the poem "Winter Sketch, Rockcliffe, Ottawa," Anne Wilkinson uses unrelenting imagery of snow to depict a community "dismembered by two worlds." Who the community is when snow arrives to "etherize" it is rendered a separate thing to whom it is the rest of the time, when its "hard arteries" are free-flowing. Wilkinson's language presents the town as a person undergoing anesthesia, the snow like an anesthetic holding it still.
The overwhelming nature of the snowfall is echoed by the number of descriptors Wilkinson uses to depict it: "polar," "frostbite," "storm of white," "tusked with icicles," "stuporous in slow white sand." As a reader, we cannot escape the snow, just as the town cannot.
The community itself as presented in the poem is divided, the men "dismembered by two worlds." To them, we can infer, the snow is largely an inconvenience, but this renders them unable to appreciate its beauties as the children do, their "uncurled ears" perceiving in the polar landscape what their elders cannot. The snow is, in truth, a protector, a "winding sheet" for "our myth-told-many-a-bed-time tale." Wilkinson uses extended metaphor to emphasize the idea of the landscape as mother or nursemaid, the snow simply a blanket enveloping it "till April swells the shroud to breast," its "milky... encrusted nipples" providing succor for the spring bloom.
There is an innocence in the children of the community which is underlined through Wilkinson's references to "Christ"; as the children "christen" their snow creations, so also do they celebrate their own innocence in the purity of the snow: making angel shapes in it, they say, " dare the snow my wings to keep." The snow blankets and conceals what is impure or apparently "hard" in the community, and makes it appear clean again.

What ideas of the Constitution were original?

The Founding Fathers wrote the Constitution. They looked at a number of sources to develop the document. They wanted a federal government that had enough power to govern the people, but not too much power so that it could become abusive.
The Magna Carta was one document that was examined. In the Magna Carta, the nobles demanded that the King guarantee the people certain rights. The Magna Carta established the idea that the King doesn’t have unlimited power. While the King agreed to consult the nobles before making decisions, it did plant the idea that the King’s power could be limited. The Petition of Right was another document that was considered. The Petition of Right emphasized the idea that common people should have a voice in their government. The English Bill of Rights was a third document that was used. The English Bill of Rights guaranteed certain rights to the people. Free elections and protecting the rights of those who are accused of crimes are examples of rights people had.
The Founding Fathers also viewed the ideas of some of the leading thinkers of the 17th century. Baron de Montesquieu believed that people were able to govern themselves. He believed in the concept of separation of powers. In our government, there are three branches of government that have different jobs. No branch of government can do it all by itself.
John Locke was a thinker that the Founding Fathers studied closely. Locke believed that a government gets its power from the people. The job of government is to protect the rights of the people. There are certain rights that all people have and that can’t be taken away by the government. These include the right to life, liberty, and the pursuit of happiness. This view can be seen in the Declaration of Independence and in the Constitution.
While the Founding Fathers looked at other documents and considered the views of other philosophers, there are some parts of the Constitution that are unique. For example, the Great Compromise created a two-house legislature. In one house, there is unequal representation for each state. The larger states have more representatives than the smaller states. In the other house, there is equal representation for each state. Another example is the Three-Fifths Compromise. The Three-Fifths Compromise states that five slaves would be counted as three people when it came time to count the number of people living in each state.
Thus, while some ideas of the Constitution were drawn from other documents or from other philosophers, there are some aspects of the Constitution that are unique to it. Additionally, some of the ideas that came from other places had to be molded to fit our system of government as outlined in the Constitution.
https://m.landofthebrave.info/bill-of-rights-1689.htm

https://www.history.com/topics/united-states-constitution/constitution

https://www.ushistory.org/gov/2.asp

Where exactly does Karl Marx or Friedrich Engels describe the eventual demise (or implosion?) of capitalism?

The inevitability of capitalism's destruction is prevalent in much of Marx's writing.  However, its direct mention can be seen in the opening chapter of Marx's and Engels's The Communist Manifesto.
An essential component of Marx's thesis is the inevitability or dialectical materialism.  He argues that history progresses in this unstoppable unfolding that allows the conditions for change to take place. Essentially, this means, that capitalism will eventually disappear.  Marx opens The Communist Manifesto with such an idea.  He believes that capitalism is progressing with so much speed that a breakdown is bound to happen:

Because there is too much civilisation, too much means of subsistence, too much industry, too much commerce. The productive forces at the disposal of society no longer tend to further the development of the conditions of bourgeois property; on the contrary, they have become too powerful for these conditions, by which they are fettered, and so soon as they overcome these fetters, they bring disorder into the whole of bourgeois society, endanger the existence of bourgeois property. The conditions of bourgeois society are too narrow to comprise the wealth created by them.

Marx sees capitalism as a "runaway train."  The industrialists' desire for wealth has created a world of "too much industry."  Marx sees this unfettered desire for wealth as unsustainable.  Eventually, a world of "too much commerce" will run out, creating the conditions for its eventual destruction.
At the same time, Marx sees capitalism's destruction in the consolidation of the people who suffer the most under it.  Marx believes that for every industrialist benefitting from capitalism, there are many more who do not.  When these individuals unify, Marx sees the implosion of capitalism as inevitable:

The lower strata of the middle class — the small tradespeople, shopkeepers, and retired tradesmen generally, the handicraftsmen and peasants — all these sink gradually into the proletariat, partly because their diminutive capital does not suffice for the scale on which Modern Industry is carried on, and is swamped in the competition with the large capitalists, partly because their specialised skill is rendered worthless by new methods of production. Thus the proletariat is recruited from all classes of the population.

The recruitment of the proletariat from "all classes of the population" is why Marx feels that capitalism is doomed. He believes that once all of those toiling under capitalism realize they are not alone and pull together as one, they will be an unstoppable force.  Marx goes on to explain that "what the bourgeoisie therefore produces, above all, are its own grave-diggers."  Each success the wealthy experience means hardship for more people.  Marx believes that the proletariat will not suffer in silence, but rather consolidate as one entity.  They will be united in their shared disdain for capitalism and resoundingly call for change.  This is the reason why capitalism's "fall and the victory of the proletariat are equally inevitable."

What is the significance of the shallop flitting away unhail'd?

The lines in which this phrase occurs are: 

 ... by the marge unhail'd 
The shallop flitteth silken sail'd, 
       Skimming down to Camelot. 

What makes these lines somewhat puzzling is that they are located in Part I of the poem and yet seem to describe the Lady of Shallot floating down the river after the curse has come upon her. However, we only discover the curse in Part II, her vision of Lancelot in Part III, and her departure for Camelot in Part IV. This means that the time sequence of the poem is not linear.
 
The lines in Part I present us with a mystery, the "royally apparelled" Lady of Shallot lying down dead in a silken bed in a "shallop" (a term meaning a small sail boat) floating down the river to Camelot. This mystery is presented to us in the present time of the poem. Parts II and III explain the events that lead up to this event, with Part II describing her life before Lancelot and Part III describing the arrival of Lancelot and how the curse is triggered. Part IV leads us back to the "present" of Part I, with the Lady floating dying and eventually dead down the river in the shallop. 
 
The mention of her departure being "unhail'd" is in a way sad, because it suggests that no one really cares about or notices her death; it emphasizes her loneliness.

The lady's tower is a grey prison. Outside the tower wall, the poet describes the many signs of life. There are fields of barley and rye. The roads running through the fields are full of people. In other words, the world outside of her tower is teeming with life. She is stuck in a drab, lifeless interior. The small boat (shallop) flows down the river. She waves but they do not see her. The shallop floats freely. In contrast, the lady is not free to move about. She is imprisoned. The other significant aspect is that she is a mystery to the people of the outside world. In the next stanza, the speaker says that only the reapers hear her in the early morning. They conclude that it is the "fairy Lady of Shallot."
She is the damsel in distress or the damsel imprisoned. Like Penelope waiting for Ulysses or Rapunzel waiting for a prince, the Lady waits for Sir Lancelot. She waits while everyone outside moves freely. The boat (shallot) moves freely and does not hail her. This emphasizes her loneliness and her dilemma of being trapped and unacknowledged. Unlike the boat, she is not free to flow toward Camelot.

How does Gretel portray innocence throughout the novel The Boy in the Striped Pajamas?

Perhaps, Gretel is more naïve than she is innocent as she lacks judgment and does not deduce what goes on behind the wire fences, the kind of person Lieutenant Kotler is, what transpires between her mother and the lieutenant, and what her father's role is in the German government. 
In Chapter 3, after Bruno's family arrives at "Out-With," Bruno talks to his sister about how unpleasant their new home is, and she agrees. Being three years older, she explains to her younger brother that Out-With is the name of the house in which they now will live. "Out with the people who lived here before us."

"It must have to do with the fact that he [the former commandant] did not do a very good job, and someone said 'out with him and let's get a man in here who can do it right,'" (Ch.3) she tells Bruno.

As they talk, Bruno mentions that the children do not look very good, either. Gretel has no idea what he means, so Bruno invites her to look out his window. When she does, Gretel does not like what she sees. There are wire and sharp spikes all around the fence. While Gretel wonders why anyone would build such "a nasty place," she concludes that it must be the countryside where food is raised somewhere. When Bruno questions her, she tells her brother that she learned in school about the countryside where there is so much land. So, this is where they must be. Then, she "shivers and turns away" and tells her brother that she is going back to her dolls in her room where the view is much nicer.
Further, Gretel enjoys feeling older as Lt. Kotler flirts with her; as a result, she naively believes that he is nice because she lets her emotions rule her. In fact, she does not really assess what a cruel, sadistic young man he is. When Gretel is with Lt. Kotler, she "...laughed hysterically and twirled her hair around her fingers...." (Ch.9)
Gretel's mother talks privately with Lt. Kotler, calling him affectionate terms, but Gretel does not seem to notice, while Bruno catches her.

"Oh, Kurt, precious, you're still here," said Mother....I have a little free time now if--Oh! Bruno! What are you doing here?" (Ch. 15)

Of course, Gretel knows nothing of mother's "afternoon naps" and is also innocent of why Lt. Kotler is transferred. Also, she does not know what lice is when she finds an egg in her hair. Later, when her father finally decides that the children must depart from "Out-With," but it is mainly because Mother wishes to return to Berlin, Gretel is unaware of this, as well.
 

Is Ezra Pound's "In a Station of the Metro" a poem? Why or why not?

How we determine what is a poem is a matter of cultural consensus. While we can determine whether something is a cat or a supernova by using various absolute scientific standards, poetry is not like biology or physics in that it depends on culturally variable types of definition. 
Ezra Pound's poem "In the Station of the Metro" was initially published in 1913 in Poetry, a literary journal. It was intended to exemplify the then-radical "Imagist" literary movement. In his manifestos and other critical works, Pound argued the heart of poetry was the "image," "that which presents an intellectual and emotional complex in an instant of time." According to this definition, "In the Station of the Metro" is an imagist poem, distilling the experience of the subway, and particularly of people standing and hanging on to straps in the subway, through a single metaphor of damp, dying petals. 
This work fits the definition of poetry in two ways. First, it is widely reprinted and taught as a poem, making it part of our cultural norms of what constitutes an example of poetry. Secondly, it fits one important critical definition of a poem. 

In Grendel, what poetic device is used in “ragged little bands that roamed the forest on foot"?

Grendel, a novel by John Gardner, gives us the classic story of the epic poem Beowulf from the monster Grendel's perspective. While Grendel is not written in poetic verse as Beowulf is, it still makes great use of literary and poetic devices. 
The specific quote you are asking about uses the poetic device of alliteration twice. Alliteration is the repetition of letters/sounds at the beginning of words that are consecutive or close to each other in a sentence or phrase. In your quote, we find repetition of the letter "r" with the words "ragged" and "roamed," as well as repetition of the letter "f" with the words "forest" and "foot." If you move a little further in the sentence your phrase is from, to "crafty witted killers that worked in teams," you will see even more alliteration with "crafty" and "killer" and "witted" and "worked."

How does Amir's relationship with his father influence his treatment of Hassan?

From Amir's point of view, Hassan is a means to an end. As a Hazara, Hassan is considered a second-class citizen by most Pashtuns, so Amir definitely doesn't see Hassan as an equal. In the novel, Amir betrays Hassan in order to win his father's esteem and affection.
We can trace Amir's heinous treatment of Hassan to his dysfunctional relationship with his father, Baba. At six-foot-five, Baba is a towering figure of a man. He is a typical Pashtun: dominant, proud, and unyielding. As a man who appreciates the fiercer side of things, Baba finds it difficult to comprehend his poetry-loving son. Realizing he has little talent for athletics, Amir must strive to gain what little paternal attention he can from Baba through other avenues. Alas, his efforts fall flat. At the yearly Buzkashi tournament, he cries when he sees a horseman trampled to death by his opponents' horses.
Later that night, he overhears Baba telling Rahim Khan that Amir is missing the necessary "mean streak" all self-respecting boys should have. Baba is ashamed Hassan has to step in to rescue Amir when the neighborhood boys tease him. Baba's last words to Rahim Khan are especially hurtful:

But something about Amir troubles me in a way that I can't express. . . If I hadn't seen the doctor pull him out of my wife with my own eyes, I'd never believe he's my son.

Baba's obvious preference for Hassan and extreme disdain for what he considers Amir's weakness leads to resentment on Amir's part. Later, Amir betrays Hassan twice in order to preserve his place in Baba's affections. The first betrayal occurs when he neglects to come to Hassan's aid during his rape. Amir's only interest is in winning the kite tournament, and he callously ignores Hassan's misery when Hassan hands him the kite he retrieved. Even though Amir notices Hassan is bleeding from between his legs, Amir decides his father's esteem is worth Hassan's suffering.
The second betrayal occurs when Amir accuses Hassan of stealing his watch and money. Ashamed of himself after his first betrayal of Hassan, Amir tries to manufacture a crisis to get rid of Hassan, a constant reminder of Amir's guilt, entirely. He imagines that, with Hassan gone, Baba will look at him with different eyes. Things don't work out as he plans, though. Unknown to Amir, Hassan is Baba's illegitimate son, and Baba is genuinely upset when the boy leaves with Ali. Far from gaining Baba's esteem, Amir falls even lower in Baba's estimation.
Due to his ambivalent and conflict-ridden relationship with Baba, Amir treats Hassan contemptuously and callously.

Why can Cherry and Ponyboy not socialize at school or other places?

The Socials, or Socs, are the wealthier kids while the Greasers are the kids from the opposite side of town with less money and fewer opportunities. Ponyboy explains how the girls from the Socs' side "looked at us like we were dirt" in much the same way the Social boys driving in their nice cars look at Greasers.
At a drive-in movie, Ponyboy and Johnny end up sitting with two girls from the Soc side. One of the girls, Cherry, seems to like Ponyboy, and they end up having a long conversation. When they stand in line together to get popcorn, Ponyboy notices the stares they are receiving since it is rare to see a "kid grease and a Socy cheerleader" together.
During their conversation, Ponyboy and Cherry agree that not all Socs are the same in much the same way that not all Greasers are the same. However, Cherry explains to Ponyboy, "if I see you in the hall at school or someplace and don't say hi, well, it's not personal or anything." The reason she can't be seen talking to Ponyboy at school is because of the unwritten social rules of class. Greasers are seen as being beneath the Socs, and to be seen hanging out with one is frowned upon by the other Socs. Cherry knows this is wrong, as does Ponyboy, but the unwritten rules are difficult to change.

How is Jem demonstrating that he is becoming an adult with textual evidence

Jem begins to mature during the beginning of Part Two and starts behaving like his morally-upright father. In chapter 14, Dill runs away from home and hides underneath Scout's bed. After discovering Dill under Scout's bed, Jem and Scout listen to Dill explain how and why he ran away. Jem understands that Dill's parents are probably worried about him and demonstrates maturity by saying,

"You oughta let your mother know where you are...You oughta let her know you’re here" (Lee, 142).

In chapter 15, Jem, Scout, and Dill watch as the Old Sarum bunch surrounds Atticus outside of Tom Robinson's cell in the Maycomb jailhouse. Jem recognizes that his father is in a dangerous situation and refuses to go home when Atticus tells him to. Jem once again demonstrates his maturity by recognizing the dangerous situation and refusing to leave his father alone. Scout describes her brother's obstinance by thinking,

We were accustomed to prompt, if not always cheerful acquiescence to Atticus’s instructions, but from the way he stood Jem was not thinking of budging (Lee, 154).

Following the Tom Robinson trial, Jem develops empathy for defenseless beings and illustrates his maturation by preventing Scout from squashing a harmless roly-poly bug in chapter 25. As Scout is about to smash the bug, Jem scowls at her. When Scout asks Jem why she isn't allowed to smash the bug, he reveals his maturation and understanding of his father's lesson regarding the importance of protecting innocent beings by saying,

"Because they don’t bother you" (Lee, 242).

In chapter 28, Scout gets yelled at from Mrs. Merriweather for coming onto the stage late and ruining the pageant. Fortunately, Jem demonstrates his maturity by attempting to comfort his sister. Scout contemplates,

She made me feel awful, but when Jem came to fetch me he was sympathetic. He said he couldn’t see my costume much from where he was sitting. How he could tell I was feeling bad under my costume I don’t know, but he said I did all right, I just came in a little late, that was all. Jem was becoming almost as good as Atticus at making you feel right when things went wrong (Lee, 262).

Single Variable Calculus, Chapter 2, 2.3, Section 2.3, Problem 58

Give an example that $\lim \limits_{x \to a} [f(x) + g(x)]$ may exist even though neither $\lim \limits_{x \to a} f(x)$ nor $\lim \limits_{x \to a} g(x)$ exists.

Suppose that $\displaystyle f(x) = \frac{2}{x}$ and $\displaystyle g(x) = \frac{-2}{x}$

$\lim \limits_{x \to 0} f(x) \text{ and } \lim \limits_{x \to 0} g(x) \quad \text{ do not exists for the functions are undefined for $$ denominator.}$

$
\begin{equation}
\begin{aligned}
& \text{However,}\\
& \lim \limits_{x \to 0}[f(x) + g(x)] && = \lim \limits_{x \to 0} f(x) \left[\frac{2}{x} + \left( -\frac{2}{x} \right) \right]\\
& \phantom{x} && = \lim \limits_{x \to 0} f(x) \left[\frac{2}{x} -\frac{2}{x} \right]\\
& \phantom{x} && = \lim \limits_{x \to 0} 0\\
& \phantom{x} && = 0
\end{aligned}
\end{equation}
$

Why was Germany's aggression successful in 1930?

1930 was a very significant year for Germany, but more specifically it was a very important year for the rise of the National Socialists (Nazis). In terms of aggression, 1930 was a powerful year of campaign, debate, and effective propaganda. These efforts in 1930 were instrumental in securing the important political positions that fortified the rise of the Nazi Party. In 1930, Wilhelm Frick was the first Nazi to become minister of a state government. Another important victory for the Nazis was securing 107 seats in the Reichstag. In 1930, the Nazis led an aggressive campaign of propaganda, which included films, street marches, demonstrations, and door-to-door dissemination of National Socialist ideals. What was this aggressive message promising, and why was it so well received?
Following the U.S. Stock Market Crash of 1929, there was a depression that gripped the world, especially Germany. In 1930, German unemployment was nearing 4 million. This same year, Hitler began to aggressively speak about the economic failure and the failure of the democratic Weimar Republic. After Germany’s serious defeat in WWI, the nation adopted a democratic system with free elections and a constitution. Hitler argued that this system was a failure. He argued that National Socialism would make Germans strong again. He promised to drive out Jews, to whom he attributed the nation’s economic and societal failure. Hitler promised to purge the leftist parasites, create jobs, help the farmer, and create a classless society full of equal opportunity. In a time when the nation was economically devastated , under-employed, and looking for someone to blame, the Germans latched on to Hitler’s solutions. The years that followed led to the rise of one of the most powerful political systems in the history of humankind.
Suggested Reading:
McDonough, Frank. Hitler and the Rise of the Nazi Party, 3rd ed., Routledge, 2014.

College Algebra, Chapter 7, 7.4, Section 7.4, Problem 26

Determine the determinant of the matrix $\displaystyle \left[ \begin{array}{cccc}
1 & 2 & 0 & 2 \\
3 & -4 & 0 & 4 \\
0 & 1 & 6 & 0 \\
1 & 0 & 2 & 0
\end{array} \right]$. State whether the matrix has an inverse, but don't calculate the inverse.

Let

$ A = \displaystyle \left[ \begin{array}{cccc}
1 & 2 & 0 & 2 \\
3 & -4 & 0 & 4 \\
0 & 1 & 6 & 0 \\
1 & 0 & 2 & 0
\end{array} \right]$

$\displaystyle \det (A) = \left[ \begin{array}{cccc}
1 & 2 & 0 & 2 \\
3 & -4 & 0 & 4 \\
0 & 1 & 6 & 0 \\
1 & 0 & 2 & 0
\end{array} \right] = 0 \left| \begin{array}{ccc}
2 & 0 & 2 \\
-4 & 0 & 4 \\
0 & 2 & 0
\end{array} \right| - 1 \left| \begin{array}{ccc}
1 & 0 & 2 \\
3 & 0 & 4 \\
1 & 2 & 0
\end{array} \right|
+ 6 \left| \begin{array}{ccc}
1 & 2 & 2 \\
3 & -4 & 4 \\
1 & 0 & 0
\end{array} \right|
+ 0 \left| \begin{array}{ccc}
1 & 2 & 0 \\
3 & -4 & 0 \\
1 & 0 & 2
\end{array} \right|
$

$\displaystyle \det (A) = -1 \left| \begin{array}{ccc}
1 & 0 & 2 \\
3 & 0 & 4 \\
1 & 2 & 0
\end{array} \right| + 6 \left| \begin{array}{ccc}
1 & 2 & 2 \\
3 & -4 & 4 \\
1 & 0 & 0
\end{array} \right|$

$\displaystyle \det (A) = -1 \left[ 1 (0 \cdot 0 - 4 \cdot 2) - 0 (3 \cdot 0 - 4 \cdot 1) + 2 (3 \cdot 2 - 1 \cdot 0) \right] + 6 \left[ 1 (-4 \cdot 0 - 4 \cdot 0) - 2 (3 \cdot 0 - 4 \cdot 1) + 2 (3 \cdot 0 - (-4) \cdot 1) \right]$

$\displaystyle \det (A) = -4 + 96$

$\displaystyle \det (A) = 92$

The given matrix has an inverse.

Single Variable Calculus, Chapter 3, 3.4, Section 3.4, Problem 23

Determine the equation of the tangent line to the curve $\displaystyle y = x + \cos x$ at the given point $(0,1)$


$
\begin{equation}
\begin{aligned}

\qquad y' =& \frac{d}{dx} (x) + \frac{d}{dx} (\cos x)
&&
\\
\\
\qquad y' =& 1- \sin x
&&

\end{aligned}
\end{equation}
$




Let $y' = m_T$ (slope of the tangent line)




$
\begin{equation}
\begin{aligned}

y' = m_T =& 1 - \sin (0)
&& \text{Substitute value of $x$}
\\
\\
m_T =& 1
&&

\end{aligned}
\end{equation}
$


Using Point Slope Form substitute the values of $x, y$ and $m_T$


$
\begin{equation}
\begin{aligned}

y - y_1 =& m (x - x_1)
\\
\\
y - 1 =& 1 (x - 0)
\\
\\
y -1 =& x
&&
\\
\\
y =& x + 1


\end{aligned}
\end{equation}
$

Looking for a quote to back up the question: what does Pip learn about being a gentleman?

Pip has tried so very hard to be a gentleman. With the assistance of Abel Magwitch's bequest, he has been able to fulfil a lifelong dream and start acting out the role of man about town. He throws himself enthusiastically into a world of fine clothes, parties, gambling, and all-round gaiety. But it's all so incredibly shallow. Pip has come to think that being a gentleman is all about what's on the outside. When Joe comes to London to pay him a visit, Pip is incredibly embarrassed by his awkward manners and simple country demeanor; poor Joe is truly a fish out of water in the big city. When Pip sees Joe, he's ashamed to discover about himself that he's turned into something of a snob.
Later on in the story, when Pip's recovering from illness, he awakes to see Joe's kindly face by his bedside. Pip is immediately overcome by remorse for the way he treated Joe earlier on his visit to London:

O Joe, you break my heart! Look angry at me, Joe. Strike me, Joe. Tell me of my ingratitude. Don’t be so good to me!’ For, Joe had actually laid his head down on the pillow at my side and put his arm round my neck, in his joy that I knew him. ‘Which dear old Pip, old chap,’ said Joe, ‘you and me was ever friends. And when you’re well enough to go out for a ride - what larks!

Joe's kindness, compassion and unbreakable friendship has shown Pip what it really means to be a gentleman. Money, clothes, an active social life––none of that means anything. What really matters is what's inside and how you treat other people.

What are the similarities and differences between "War Photographer" by Carol Ann Duffy and "Driving through Minnesota During the Hanoi Bombings" by Robert Bly?

Both Carol Ann Duffy's "War Photographer" and Robert Bly's "Driving through Minnesota During the Hanoi Bombings" are poems that seem to respond to the Vietnam War, and both poems were published in the mid-1980s. The poems both contrast an ordinary setting to a war setting, and both speakers reflect on the impact of war.
Duffy's war photographer, as we can tell from the title and the details early in the poem, has taken photos on the warfront and is not developing his images. The photographer takes his task very seriously. The speaker explains,

The only light is red and softly glows,
as though this were a church and he
a priest preparing to intone a Mass (3–5).

The photographer sees his work as sacred. Indeed, he is calling up images of the dead. The speaker lists places like "Belfast," "Beirut," and "Phonm Pehn," which are places related to different conflicts (the last one is in Vietnam). It is clear here that perhaps the poem is reflecting on global war on a wider scale than Bly does in his poem on Vietnam and a specific bombing event.
A major point of similarity between the two poems is evident in Duffy's second stanza, when the speaker reflects on the photographer's life at home and his life at war. The speaker writes,

Rural England. Home again
to ordinary pain which simple weather can dispel,
to fields which don’t explode beneath the feet
of running children in a nightmare heat (9–12).

The photographer's "Home" in "Rural England" is merely one of "ordinary pain." A striking image contrasts the fields of England to those of war, which would "explode . . . in a nightmare heat." The photographer is much safer now, yet he is possibly more affected by what he has seen as he recalls the events through his pictures. The speaker says his hands "tremble," even though they did not when he was on the front.
The third stanza reveals the speaker's memories associated with the images. Here, we see the more visceral depiction of war that was captured forever in the photos. As he sees the image of a man's face form in his dark room,

He remembers the cries
of this man’s wife, how he sought approval
without words to do what someone must
and how the blood stained into foreign dust (15–18).

The photographer is brought back to the moment he snapped this image. His memories include the wife of this man, now "half-ghost," crying out, and the photographer's feeling that he "must" do this duty. The impact of war is felt both in the photo and in "the blood stained into foreign dust." And yet, when the speaker closes the poem, it is the photographer's doubt and cynicism that rule. Although he imagines people seeing the "five or six" photos his editor will publish, the speaker knows their impact will not be felt by viewers:

From the aeroplane he stares impassively at where
he earns his living and they do not care (23–24).

This is a strong statement that indicates that the public cannot fully understand, not having been on the front, and therefore can never truly "care" about war in the way the photographer can.
Robert Bly's "Driving through Minnesota During the Hanoi Bombings," as I said, is more specific in its context. However, it maintains similar themes to Duffy's poem in the sense that Bly contrasts the homefront to the warfront and reflects on the war in ways that show its direct impact on the subject/speaker of the poem. The speaker shifts rather suddenly early in the poem from a discussion of turkeys and the environment to a seeming reflection on war:

We drive between lakes just turning green;
Late June. The white turkeys have been moved
A second time to new grass.
How long the seconds are in great pain!
Terror just before death,
Shoulders torn, shot
From helicopters (1–7).

The speaker and a companion are simply driving, but the speaker starts thinking about the "great pain," "Terror," and "death" associated with the bombings. The speaker includes a small bit of dialogue that may be related to an experience he has had at war or something he saw in an interview:


“I saw the boy
being tortured with a telephone generator,”
The sergeant said.
“I felt sorry for him
And blew his head off with a shotgun.”
These instants become crystals,
Particles
The grass cannot dissolve (7–14).



The sergeant's reasoning is disturbing, as is the accompanying imagery. It seems ironic that he would kill someone he pitied. Significantly, the speaker notes that the memories "cannot dissolve." Just as for the photographer in Duffy's poem, the impacts of war stay with the speaker despite his ordinary surroundings.

In the second half of the poem, the speaker continues,


Our own gaiety
Will end up
In Asia, and you will look down in your cup
And see
Black Starfighters.
Our own cities were the ones we wanted to bomb!
Therefore we will have to
Go far away
To atone
For the suffering of the stringy-chested
And the short rice-fed ones, quivering
In the helicopter like wild animals,
Shot in the chest, taken back to be questioned (14–26).



The first part of this section of the poem suggests that even happy times in the present, at home, can trigger memories of the war. The attempt to "Go far away / To atone" is probably unsuccessful, since most of the poem's tone seems remorseful and melancholy. In that sense, both poems have a similar tone.

Both Duffy's and Bly's poems are about the impact of war on those who have witnessed or experienced war in some capacity. The poem's tones suggest the lasting and inevitable way that the experiences stay with the subjects of the poem. Duffy's poem further implies that those who do not experience war are not impacted much at all.

Calculus of a Single Variable, Chapter 8, 8.2, Section 8.2, Problem 15

Recall that indefinite integral follows int f(x) dx = F(x) +C where:
f(x) as the integrand function
F(x) as the antiderivative of f(x)
C as the constant of integration.
For the given integral problem: int t ln(t+1) dt , we may apply u-substitution by letting:
u = t+1 that can be rearrange as t = u-1 .
The derivative of u is du= dt .
Plug-in the values, we get:
int t ln(t+1) dt= int (u-1) ln(u) du
Apply integration by parts: int f*g'=f*g - int g*f' .
We may let:
f =ln(u) then f' =(du)/u
g' =u-1 du then g=u^2/2 -u
Note: g =int g' = int (u+1) du .
int (u-1) du =int (u) du- int (1) du
= u^(1+1)/(1+1) - 1u
= u^2/2 - u
Applying the formula for integration by parts, we set it up as:
int (u-1) ln(u) du = ln(u) * (u^2/2-u) - int(u^2/2-u) *(du)/u
=(u^2ln(u))/2-u*ln(u) - int(u^2/(2u)-u/u) du
=(u^2ln(u))/2-u*ln(u) - int(u/2-1) du
For the integral part: int (u/2-1) du, we apply the basic integration property: int (u-v) dx = int (u) dx - int (v) dx .
int(u/2-1) du=int(u/2) du-int (1) du
= 1/2 int u - 1 int du
= 1/2*(u^2/2) - 1*u+C
= u^2/4 -u+C
Applying int(u/2-1) du=u^2/4 -u+C , we get:
int (u-1) ln(u) du =(u^2ln(u))/2-uln(u) - int(u/2-1) du
=(u^2ln(u))/2-u*ln(u) - [u^2/4 -u]+C
=(u^2ln(u))/2-u*ln(u) - u^2/4 +u+C
Plug-in u = t+1 on (u^2ln(u))/2-u*ln(u) - u^2/4 +u+C , we get the complete indefinite integral as:
int t ln(t+1) dt=((t+1)^2ln(t+1))/2-(t+1)ln(t+1) - (t+1)^2/4 +t+1+C
OR [(t+1)^2/2-t-1]ln(t+1) - (t+1)^2/4 +t+1+C