What's the main idea in "O Captain! My Captain"?

It is well known that Whitman's "O Captain! my Captain!" is a lament for the death of Abraham Lincoln. Even without that knowledge, however, the poem remains effective and moving, in large part because the idea and emotions it conveys are not necessarily tied to that singular situation.
The main idea, or point of emphasis, in this poem is underlined through Whitman's use of repetition: the Captain is "fallen cold and dead." Whitman repeats this phrase three times, and it is the final line in the poem and thus the idea retained by the reader. The death of the captain has not been for nothing—after all, the "fearful trip is done," "the prize we sought is won," and the people are "all exulting." So, the tone of the poem, while melancholy, is not without its lighter elements. The captain has died in achieving his goals, and the people recognize that, with "the flag . . . flung" for the fallen captain, while "the bugle trills." In recognition of the captain's sacrifice, there are "bouquets and ribbon'd wreaths," and the shores are "a-crowding."
We know that, for the speaker himself, this "victory" is not yet sufficient to override his sadness over the loss of his captain. He moves "with mournful tread," his heart "bleeding drops of red." However, there is a glimmer of hope at the end of the poem that, in fact, he does recognize that the sacrifice may have been worth it. He encourages the celebration of victory which validates his captain's sacrifice: "Exult O shores, and ring O bells!" So, arguably, the key idea in this poem is that to die for a "dream" is a sacrifice which may ultimately be worth it, if the "ship is anchor'd safe and sound," whatever the sadness suffered for the loss of a "father."

Walt Whitman's poem "O Captain! My Captain!" is an elegy poem, written in tribute to Abraham Lincoln in the year that he died, 1865. It is an extended metaphor and contains three stanzas. The main idea of the poem is that the civil war has ended, which is a cause for celebration, and the reason it is over and won is because of the "ship's captain", Abraham Lincoln, who was instrumental in that war, and now has died without really being able to enjoy the fruits of his labor. 
Using the imagery of a ship, the first stanza talks about the celebration going on because the "prize we sought is won." This is referring to the end of the civil war. At the end of the stanza, the poet laments the death of the captain. 

"But O heart! heart! heart! O the bleeding drops of red,
Where on the deck my Captain lies, Fallen cold and dead."

The second stanza is a plea for the captain to rise up, to join in the celebrations that are for him, and to not be gone from them forever. 
In the third stanza, the poet seems to have accepted that the captain is indeed, dead, and isn't coming back. He is mourning the loss even as those around him celebrate the victory. 

How can I write an essay that analyzes the social or environmental factors at work in examples of juvenile delinquency in the newspaper?

To complete this assignment, your best strategy might be to choose a specific form of juvenile delinquency or cause of it as your focus so that you can narrow your search and write a coherent essay. In my experience of over 20 years of university teaching, the problem students are most likely to face with this sort of assignment is unfocused writing that simply summarizes seeming random results from a search engine. 
A good starting point might be looking at a recent study on juvenile offenders in Los Angeles. This study shows that over 30 percent of juvenile offenders are re-arrested within a year. It also finds that over 90 percent of juvenile offenders in the Los Angeles system have some sort of mental health issues. 
You could use this information to focus your essay on the prevalence of mental health issues among juvenile offenders in Los Angeles, using a internet search engine to do a Boolean search for three articles in the Los Angeles Times about individual cases of juvenile offenders, and for each case, show how mental health issues, substance abuse, and a chaotic home environment contributed to their criminal activities. To make the essay even more focused, you could restrict your search to one specific type of crime, such as violent crime or selling drugs.

An asteroid of mass m orbits the sun (mass M ) on a parabolic trajectory. What is the expression that relates its distance of closest approach d to its orbital velocity v at the time of closest approach?

I will solve this problem in a general way that would work for any one body parabolic, elliptic or circular orbits. The total energy of an arbitrary classical orbit is derived from its Lagrangian. It is:
E=T+V=1/2m((dr)/(dt))^2+l^2/(2mr^2)+U(r)
l is the angular momentum and r is the radial distance, r=d at closest approach.
For the gravitational potential:
U(r)=-(GmM)/r|_(r=d)=-(GmM)/d
For a parabolic orbit E=0 .
1/2m((dr)/(dt))^2+l^2/(2md^2)-(GmM)/d=0
At the moment of closest approach the asteroid is at a minimum in r , so the change in r , (dr)/(dt)=0 . Also, l is exactly tangential so l=r xx p=dmv .
(dmv)^2/(2md^2)=(GmM)/d
1/2 mv^2=(GmM)/d
Notice this relation simplified to the same results one would get as setting its kinetic energy and potential energy equal to each other. This only happened because conveniently the asteroid was at the distance of closest approach.
d=(2Gm)/v^2

How does the poet depict the Ireland before the event?

"Easter 1916" by William Butler Yeats is a poem responding to the "Easter Rising," an event in the long struggle by the Irish for independence from England that took place in April 1916. In the decades immediately preceding the Easter Rising, this struggle had been mainly pursued through legal avenues and peaceful protests, but as conflicts between those in favor of Home Rule and Unionists intensified, Ireland moved to the brink of civil war.
Yeats's poem shows a gradual evolution in Irish life before the Easter Rising. It describes the Republican leaders having ordinary lives, with Constance Markievicz enjoying the relaxing leisure pursuits of an aristocratic woman (hunting rabbits on horseback) and Patrick Pearse and Thomas MacDonough portrayed as poets pursuing their art. The intensification of the political conflict transforms them, with Markievicz becoming argumentative and "shrill" rather than merely being decorative and feminine (a change of which the narrator disapproves) and the men also being "changed utterly" from people involved in ordinary life to something both noble and terrifying.
The third stanza suggests Ireland itself was seen as having a certain tranquil pastoral beauty which the rebellion changed, just as a horse and rider can scare away the birds floating peacefully on a stream.

What are Urim and Thummim?

The Urim and Thummim appear quite early in the book. They are a pair of stones that are given to Santiago by the king Melchizedek. The stones themselves are not large, and Santiago often takes them in and out of a pouch or a pocket. One stone is white, and the other stone is black. The colors represent "yes" and "no." Before giving Santiago the stones, the king tells Santiago that in order to find the treasure, Santiago must follow the omens.

"In order to find the treasure, you will have to follow the omens. God has prepared a path for everyone to follow. You just have to read the omens that he left for you."

Santiago remembers something about omens that his grandfather told him, and the king practically reads Santiago's thoughts. The king realizes that Santiago might need some help interpreting the omens in order to know where to go or when to go. Melchizedek then gives Santiago the Urim and Thummim stones and tells Santiago that they will help with the omens. The king then specifies that Santiago is to ask the stones objective questions and to try to use his own decisions whenever possible.

"They are called Urim and Thummim. The black signifies 'yes,' and the white 'no.' When you are unable to read the omens, they will help you to do so. Always ask an objective question."

What is Station Eleven the novel about? How would you describe it to someone and why? Who is the main character in the novel? What is the purpose of the Traveling Symphony and Shakespeare Company? How does the graphic novel, Station Eleven, work with or against the novel itself?

Emily St. John Mandel's Station Eleven is a novel about a pandemic that swiftly wipes out most of the world's population. The novel follows several characters before, during, and after the pandemic hits. I would describe this book as a post-apocalyptic novel and a work of speculative fiction, because it speculates on what would happen and how people would react and adapt if a catastrophic plague spread across the world.
There are several characters who could be considered main characters. The novel begins with Jeevan, a young student who aspires to be an EMT; he is attending a production of King Lear starring a famous actor named Arthur Leandre. The actor dies of a heart attack on stage, and soon after, Jeevan receives a call from a friend who works in a hospital, breaking the news about the pandemic. Also at the theater the night of King Lear is a child actor named Kirsten Raymonde. She becomes, essentially, the central character of the novel when we pick up with her life after the pandemic, when she is part of a traveling theater group that performs Shakespeare's plays for the small settlements of people that remain. Another major character is Miranda, who was once married to Arthur. Miranda is especially important because she is the author of the Station Eleven graphic novels. The novels are given to Kirsten by Arthur when they work on King Lear together. Throughout the novel, we follow these characters' lives, some of which end during the pandemic.
The Traveling Symphony is important because it suggests that art and culture always have a place in the world, regardless of how dire the circumstances may be. The actors and musicians believe that their role is to provide therapeutic art and beauty to the remaining survivors. The Station Eleven graphic novels, like Shakespeare's plays, live beyond the pandemic. They offer an image of an alternate universe, which is what the post-pandemic world feels like to the characters.

What makes the ending of “The Interlopers” surprising? Has Saki prepared readers for the ending, or has he led readers to expect a different kind of ending?

Two things that make the ending surprising are its suddenness and tragic irony. Saki prepares the way for this ending by painting a picture early on of the wildness in the forest that night and by describing how, even though the two men hate each other, they can't kill each other when "face to face."
The ending is surprising—even shocking—because it is so sudden. The ending is comprised of one single spoken (not yelled) word: "Wolves." This one word is preceded by only a single word, "No," accompanied by wildly fearful laughter full of irony, "the idiotic chattering laugh of a man unstrung with hideous fear."
The ending is shockingly surprising also because it ironically follows such peacemaking. In the presence of each other's suffering and courage, the men end their feud and decide they'll be friends and share hospitality; they'll share hospitality and friendliness, concern, and care. Each pledges to himself and the other that when his men come to the rescue, they shall free the other trapped man first; they shall save the new friend before the master.

"Neighbour," [Ulrich] said presently. . . "If my men are the first to come you shall be the first to be helped, as though you were my guest. We have quarrelled like devils all our lives. . . I've come to think we've been rather fools; there are better things in life than getting the better of a boundary dispute."

Saki prepares the way for this ending—he does not trick us with an unprepared (or ill-prepared) ending. Early on, he establishes that it is a wild night among the animals of the forest on this stormy "wind-scourged winter night," unnaturally disturbed by poachers, thereby paving the way for the sudden appearance of the wolves. Saki prepares us for encountering an ironic twist in the ending through presenting the double irony of having enemies trapped beneath a beech branch—held helplessly together—when moments before they had been "man to man" and "face to face," each intent on the death of the other yet unable to kill.

The two enemies stood glaring at one another for a long silent moment. Each had a rifle in his hand, each had hate in his heart and murder uppermost in his mind. . . [A] man who has been brought up under the code of a restraining civilisation cannot easily nerve himself to shoot down his neighbour in cold blood.

Saki also prepares us by presenting the ironic twist that, having mended their feud and become friends, they are still trapped together and awaiting either rescue or death: rescue, if their men find them, death beneath the branch in winter cold if they do not. It does not occur to the men to consider the ironic twist to their death Saki has prepared for them: wild wolves.