Describe the Malay mancatcher.

Readers don't get too much detail about the Malay mancatcher. In fact, it isn't described in any kind of detail prior to the trap going off. We are told that Rainsford saw a huge dead tree, and he quickly set to work with all of his energy. We have no idea what he is building, and Rainsford hides a few hundred feet away after completing his project. General Zaroff eventually comes into the area, and he is very intent on stalking Rainsford. He is so intent, in fact, that he doesn't see the trap's trigger mechanism.

So intent was the Cossack on his stalking that he was upon the thing Rainsford had made before he saw it. His foot touched the protruding bough that was the trigger.

Unfortunately for Rainsford, Zaroff has a danger sense as good as Spider Man's "spidey sense." Zaroff jumps back just as the delicately balanced dead tree falls down from the living tree. Basically, a Malay mancatcher is a trap that is designed to smash a person underneath a large, falling dead tree.

But he was not quite quick enough; the dead tree, delicately adjusted to rest on the cut living one, crashed down and struck the general a glancing blow on the shoulder as it fell; but for his alertness, he must have been smashed beneath it.

The general receives a glancing blow, and he then calls out a congratulations to Rainsford.

"Rainsford," called the general, "if you are within sound of my voice, as I suppose you are, let me congratulate you. Not many men know how to make a Malay mancatcher. Luckily for me I, too, have hunted in Malacca."

After General Zaroff narrowly discovers Rainsford hiding in a tree, the general walks away, and Rainsford climbs down. About three hundred yards from his hiding place, Rainsford finds a huge dead tree leaning against a smaller living tree. Rainford immediately throws off his sack of food and begins making a Malay mancatcher. The massive dead tree is delicately balanced on the living tree, and there is a "protruding bough" that acts as the trigger. Rainsford watches from a distance as General Zaroff accidentally steps on the trigger, which sends the massive dead tree falling down. The general narrowly escapes being crushed by the dead tree but injures his shoulder when it glances off of him. Despite his injury, General Zaroff is impressed with Rainsford's ingenuity and recognizes that the trap was a Malay mancatcher. General Zaroff then congratulates Rainford for setting the dangerous trap and walks back to his chateau to dress his wounds.

Who can help me with an analysis and a plot summary on Professor Unrat by Heinrich Mann?

The story by Heinrich Mann (brother of the more famous Thomas) dates from 1905. It is known to non-German-speaking people mainly through its famous film adaptation from 1930, The Blue Angel, with Marlene Dietrich and Emil Jannings.
In the novel, Professor Raat is a stuffy, straitlaced high school teacher who delights in disciplining and correcting his students in an angry, demeaning way. You might wish to compare him with similar old-fashioned teachers in literature who enjoy insulting and humiliating kids in class, such as Mr. Crocker-Harris in Terence Rattigan's The Browning Version. The students hate Professor Raat , and one of them adds the prefix "Un" to Raat's name written on the cover of a copybook. In German, "Raat" and "Rat" are pronounced identically, and the word Unrat means filth, garbage.
Raat becomes obsessed with a beautiful cabaret dancer named Rosa, who is probably a prostitute. The obsession ends up being Raat's undoing, and though he marries Rosa, it's clear that she is seeing other men. Raat has lost his respectable teaching job, has blown all his money on Rosa, and has basically destroyed his own life.
You can look into the question of whether these plot elements were already common in European literature in the early twentieth century, or whether this was a seminal work of fiction that perhaps created what became clichés. Does Mann see Raat's obsession with Rosa as purely destructive, or is it liberating to him as well, freeing him from the constrictions of a false and repressed life? Does he actually become a better or happier person when he links his fate to her, or is he throwing away a valuable life and simply making a fool of himself? These questions and issues form the heart of the novel's theme.

How did ordinary people react to Henry VIII's changes in 1536?

1536 was an important year in the reign of Henry VIII. He went from being the handsome, popular, athletic young king of his earlier reign to a fat, paranoid tyrant who mercilessly destroyed anyone opposing his firm, unbending will. This was the year in which Henry sent his second wife, Anne Boleyn, to the block on a trumped-up charge of adultery. Anne was widely despised by the English people as a home-wrecking gold-digger, so it's fair to assume that her decapitation was a source of widespread joy and merriment throughout the land.
Other actions of the tyrant king were less popular, however. The Dissolution of the Monasteries generated fierce resistance from devotees of the old religion, especially in the North of England. The Monasteries weren't simply places of devotion and worship; they played a vital role in the provision of alms to the poor. They were a kind of welfare state in miniature, giving much-needed help to local people when times were bad.
But Henry saw the monasteries and their extensive land-holdings as a source of rich pickings. As he was now head of the Church of England, he felt entitled to seize these valuable lands for himself and sell them off to his supporters for vast sums of money. Most of Henry's subjects went along with the changes, albeit reluctantly. But in the North of England, a full-scale rebellion broke out, which came to be known as the Pilgrimage of Grace.
Upwards of 50,000 men participated in the uprising, vastly outnumbering Henry's forces. The king had no choice but to compromise, and offered the rebels a deal, which they gladly accepted. However, Henry had no intention of abiding by any agreement that would compromise his sovereignty as king. So he bided his time, and when the moment was right, crushed the rebels mercilessly, brutally executing the rebellion's ring-leaders and laying waste to entire villages as part of a campaign of bloody terror.

In O'Connor's "A Good Man Is Hard to Find," what type of man is the Misfit?

In her attempt to plead for her life—and maybe the lives of her family—the grandmother repeatedly calls the Misfit a “good man.” The Misfit, in response, assures her that he is not a good man, and that the only “pleasure” in life is “meanness.” The Misfit is a tortured soul, who believes that the world is out to get him. He also struggles with religious faith; the only time the Misfit gets visibly upset is when he wishes he would have been there to witness Jesus’ miracles or crucifixion.
Despite the surface impression that the Misfit is a sadistic criminal, his actions in the story are rational. At first, the Misfit and his two henchmen help the family with their overturned car. While it is unclear whether the Misfit intended to kill the family from the beginning, one could argue that he did not based on his statement to the grandmother:

it would have been better for all of you, lady, if you hadn't of reckernized me.

This suggests that the only reason the Misfit has to murder the family is because of her identification. If the grandmother had’nt suddenly proclaimed the man’s identity, it is possible that the Misfit would have just left the family in the wilderness or perhaps even traded cars with them.
This is further indicated after he shoots the grandmother. When he makes his famous remark about the grandmother being a good woman if someone would have shot her every minute of her life, one of the Misfit’s accomplices says that sounds fun. The Misfit dryly replies, “Shut up, Bobby Lee. It’s no real pleasure in life.” This statement suggests that the Misfit did not enjoy killing the family or the grandmother, but rather sees it as a necessity. Although the Misfit’s morals are not the same as most people, he does seem to have a kind of code for himself.

In Flannery O'Connor's "A Good Man Is Hard to Find," the Misfit is an escaped convict who has been in jail for murdering his father. Of course, the Misfit claims that his father "died in nineteen ought nineteen of the epidemic flu" and that he is innocent. When the grandmother asks the escapee why he thinks he went to jail, though, he says that he can't remember. It is interesting how he describes himself because he mentions many normal life experiences that he has had. For example, the Misfit says that he served in the armed forces, was married twice, and has worked on railroads, on farms, and as an undertaker. These jobs all seem honorable compared to a criminal's life and prison. However, what the Misfit says about himself is different than how he acts. He and his friends kill a young family of four along with the grandmother, which doesn't seem consistent with any type of normal or honorable life. Based on the fact that actions speak louder than words, the Misfit, therefore, is not only a murderer, but he is also a liar to himself and others.

What does Ivan do the first time he enters the exhibit?

Do you mean the mall exhibit or the zoo exhibit?When Ivan first sees the cage at the mall, he is relieved. He had been living with Mack at Mack's house since he was a baby. But as he grew, he found it hard to maneuver around Mack's place without disruption. Ivan says,

"When I saw my new domain, I was thrilled, and who wouldn't have been? It had no furniture to break. No glasses to smash. No toilets to drop Mack's keys into."

Ivan also says,

"I was relieved to have my own place."

He notes, in particular, that his "new domain" has its own tire swing.So, to Ivan, his cage at the mall is, at first, an improvement over his previous circumstances living with Mack. Ivan referred to that time as his "life as a human." Being at the zoo allows him to be more like a gorilla -- but not entirely.Later in the book, when Ivan is taken to the zoo by Maya, he spends some time alone in a cage, isolated from the main gorilla exhibit by a glass door. He watches the other gorillas, and they in turn observe him. He learns the name of one of the gorillas. She is Kinyani.When Maya opens the glass door, Ivan first spends time absorbing all the new sensory impressions the outdoor exhibit provides him:

"Sky.
Grass.
Tree.
Ant. 
Stick.
Bird. 
Dirt.
Cloud. 
Wind.
Flower.
Rock. 
Rain."

Soon after, he makes his first contact with the other gorilla residents. It does not go well. Kinyani chases him and throws a stick. He cowers and returns to his cage. He cannot remember how to properly interact with other gorillas at first, especially as a full-grown silverback male. His long-term social isolation at the mall has taken its toll.Ivan soon tries again, however, and the next day intimidates a juvenile male who is eyeing his food and then builds a nest for himself. This is his first step toward assimilating into the gorilla group.

Single Variable Calculus, Chapter 7, 7.6, Section 7.6, Problem 34

Determine the derivative of the function $\displaystyle y = \tan^{-1} \left( \frac{x}{a} \right) + \ln \sqrt{\frac{x-a}{x+a}}$ and simplify if possible.
If $\displaystyle y = \tan^{-1}\left( \frac{x}{a} \right) + \ln \sqrt{\frac{x-a}{x+a}}$, then...

$
\begin{equation}
\begin{aligned}
y' &= \frac{1}{1 + \left( \frac{x}{a} \right)^2} \left( \frac{1}{a} \right) + \frac{\frac{d}{dx}\left( \sqrt{\frac{x-a}{x+a}}\right)}{\sqrt{\frac{x-a}{x+a}}}\\
\\
y' &= \frac{1}{1 + \frac{x^2}{a^2}} \left( \frac{1}{a} \right) + \frac{\frac{1}{2\sqrt{\frac{x-a}{x+a}}}\cdot \left[ \frac{(x+a)(1)-(x-a)(1)}{(x+a)^2} \right] }{\sqrt{\frac{x-a}{x+a}}}\\
\\
y' &= \frac{a}{a^2 + x^2} + \frac{a}{\left( \frac{x-a}{x+a} \right)(x+a)^2}\\
\\
y' &= \frac{a}{a^2 + x^2} + \frac{a}{(x-a)(x+a)}\\
\\
y' &= \frac{a}{a^2 + x^2} + \frac{a}{x^2 - a^2}
\end{aligned}
\end{equation}
$

In Act 1 of A Doll's House Mrs. Linde describes Nora as a 'child.' Is this assessment of Nora's state of development valid?

The first impulse is to agree with Linde and say that Nora is, indeed, a "child." However, upon a deeper reading into Nora's character,  it would be unfair to think that. 
Linde, as well as everyone else mentioned in the play, is only aware of who Nora is through the image that Nora chooses to give of herself; that of a carefree, immature, playful and ornamental part of the household. It is no surprise that Linde would think of Nora exactly as the type of character that Nora so eagerly portrays.
Still, after having been friends with Nora for years, one must wonder why Linde continues to assess Nora's character based on these external traits. The answer to this is that Linde had not learn about the sacrifice that Nora had to make years earlier in order to save the life of her husband. Entering in a business loan deal with Krogstad,a man who is beneath her husband's own status, and to do this behind her husband's back, was beginning to get back at Nora in a very bad way. 
Therefore, Nora was, indeed, going through a very difficult situation that would have required a huge amount of "adulting" to do, that is, she would have had to make choices and decisions that a mere "child" or immature person could have never been able to do. Hence, Linde was not being 100% fair when she called Nora a "child." 
Remember also that Mrs. Linde and Nora had not seen one another in years by the time that Linde visits Nora, hoping to get a job at the bank where Torvald works. Linde has fallen in hard times, is much older than Nora, and has gone through terrible vicissitudes in life that have rendered her a very objective, no-nonsense type of person. 
Linde had always known Nora for being sort of an opposite of Linde: Nora had not suffered, in Linde's opinion, any of the life tragedies that make people grow up and mature. To Linde, Nora had always been given everything that she wanted, and her problems are minor, at least compared to those that Linde has gone through.

How kind you are, Nora, to be so anxious to help me! It is doubly kind in you, for you know so little of the burdens and troubles of life.

To this, Nora seems to disagree, and then Linde explains

Linde [smiling] My dear! Small household cares and that sort of thing!--You are a child, Nora.

Nora disagrees, and resents that Linde, of all people, would think such an opinion of her. In fact, we see Nora resenting more and more that image that people have made of her, even though she has worked more than hard to build that image all by herself.