What are some of the main themes explored in Art Spiegelman's graphic novel, 'Maus'?

Maus is an iconic graphic novel by Art Spiegelman that chronicles the tale of Vladek Spiegelman, a Jew who survived Nazi Germany. Vladek is Art Spiegelman's father, and the story is narrated by Art as Vladek tells him his story.
The book can be considered a historical memoir, and many of the themes in the book lean on history to derive meaning. The tale not only tells Vladek's story, but also the story of the father-son relationship between Art and Vladek. Spiegelman uses historical plot structures of World War Two history and the father-son relationship to craft a few main themes throughout the work.
 
Alienation between humans; Racism
With much of the story set in Nazi Germany, it is not surprising that racism is a central theme in Maus. Spiegelman anthropomorphizes various animals to represent different ethnic races. For example, people of German descent are drawn as cats, those of Polish descent are drawn as pigs, and those of Jewish descent are drawn as mice. This representation is a tool Spiegelman uses to show the fundamental lack of understanding between humans during that time. Though in reality humans are all in the same species (homo sapiens), he draws them as entirely different creatures. Spiegelman's choice to draw his characters this way demonstrates the distance that opened between different ethnic groups during WWII as a result of the Nazi regime. 
 
Intergenerational familial misunderstanding
Throughout the novel, Vladek's story pauses and readers get a glimpse into the relationship between Art and Vladek. Often fraught with tension and disagreement, their relationship is frequently one of conflict. This narrative tension is juxtaposed with the very basis of the book: Art is choosing to write his father's story and clearly loves his father. Despite Art's deep love for his father, misunderstanding remains between them.
 
The interplay of memory and guilt
Two important characters die in Maus. Anya, Vladek's wife, and Richieu, Vladek and Anya's first son. Both of these characters ground Vladek's entire narrative. Within Vladek's story in Germany, they motivate and give him hope throughout his suffering in Nazi concentration camps. Later, as Vladek tells Art his story, they are conspicuously absent.  Both Vladek and Art suffer tremendous guilt over the death of these two family members. Both Anya and Richieu died due the Nazi regime and its repercussions. Art and Vladek did not cause their deaths, but still feel guilty. The particular kind of guilt they feel may be categorized as a type of survivor's guilt for making it through while their family members did not.
 

In Newjack by Ted Conover, what do you think are the lessons that can be learned from this book?

There are many lessons that can be learned through the reading of Newjack. This is a first-hand account of what it is like to be a rookie corrections officer in the maximum security prison Sing Sing. It is easy for society to forget about an individual once sentencing has taken place. However, what many fail to realize is that a large portion of these individuals will one day be released. The main question should be: will they be better or worse? Therefore, the overall lesson to consider is the need for prison reform.
To be more specific, we can look at four aspects. First, we can learn what it is like to be a corrections officer and the dangers that are faced each day. Second, we can explore overcrowding in our prison system and the effect it has on the inmate population. Next, we can research different aspects of sentencing reform and rehabilitation programs. Finally, we can discuss the issue of mental illness in the prison system. Each aforementioned lesson can be viewed from the perspective of either the corrections officer or the inmate.
For example, if we focus on mental illness, we can learn that in 2005, more than half of jail and prison inmates had a mental health problem. Is incarceration the answer for those who suffer mental illness? Are correction facilities equipped and trained to handle issues of mental health? Based on the book and my own experience working in corrections, the answer would be no.
Below you will find a link to the Bureau of Justice Statistics that discusses the mental health issues faced in our jails and prisons.
http://tedconover.com/book-newjack/

I'd like to make it clear that the above question is an opinion question.  The lessons that I learned from this book might be different from what another reader thinks.  The key to answering the question is defending what you think.  
One lesson that I learned from the book is that referring to prisons as "rehabilitation centers" is an egregious error.  I'm certain that some inmates are rehabilitated through the prison system, but after reading Conover's book, I no longer assume much rehabilitation is happening.  Near the beginning of the book Conover writes about how the prison system is equivalent to a storage facility for people.  

"Because in reality . . .  rehabilitation is not our job. The truth of it is that we are warehousers of human beings." And the prison was, above all, a storage unit.

The above section of the book really stuck with me as I read the book because it is a very dehumanizing thought.  People put inanimate, non-living things into storage units.  We put things in them that we care about, but we don't care enough about it to have it around us all the time.  That dehumanizing lesson/theme is present throughout the book.  Much of what Conover sees among his fellow guards is that they simply do not view the inmates as people.  This concept really hit home for me when I read that many CO's refer to sick inmates as "bugs" and their medicine as "bug juice."  Conover constantly works to always see the humanity in the men that he is charge of, but it's tough for him as well.  For me, the big lesson from the book is the importance of keeping a person's humanity at the forefront of your mind.  

Describe the place Holmes and Watson were investigating.

Holmes and Watson were investigating the office of the League of the Red-Headed Men. Wilson describes it as furnished with nothing but several wooden chairs and a deal table. (A deal table is a crude table made of wooden planks, somewhat like a picnic table.) The description of the room shows it was cheaply and scantily furnished.
Nevertheless, Wilson takes the four-pound-a-week, four-hour-a-day job in this office copying out the Encyclopedia Britannica because it is such a high-paying job for very easy work. He is locked into the office for the duration of his shift and told he will be fired if he leaves. He has copied out most of A in the encyclopedia and is looking forward to B when suddenly he finds a sign on the office door saying that the League is dissolved.

In Hoot, how are Beatrice's and Roy's families similar? Different?

Beatrice and Roy have slightly similar families, but in most ways their families are different. Both Beatrice and Roy are their biological parents' only children. Both Beatrice's and Roy's fathers have been high achievers in their professions. Leon Leep was a professional basketball player, and Roy's father has received multiple promotions within the Department of Justice. Of course, both families live fairly near each other in Coconut Cove, Florida, and their children attend the same school.
Beyond those few similarities, however, the families stand in stark contrast to each other. Roy's parents are nurturing and loving. They commend him when he does something good, they discipline or reprimand him when he does something wrong, and they help him think through tough issues. His mother and father seem to agree about most things and don't quarrel much. Roy's father works outside the home, while his mother doesn't. They go on family outings, eat dinner, and spend Sundays together. His parents don't hover over him, though. They allow him enough freedom to solve his problems and grow in the process. In short, they represent a functional family.
Beatrice's family is dysfunctional. Her parents quarrel and even become physically violent with each other. They are a blended family; Lonna is Beatrice's stepmother. Beatrice has never bonded with Lonna, and Lonna doesn't want her son around. Leon seems depressed and may be an alcoholic. He doesn't work and seems to have no practical life skills or healthy interests. Lonna works in the evenings. The family doesn't seem to do things together or enjoy each other's company. Beatrice makes supper for her father each night because she doesn't think he's capable of doing it for himself. 
Beatrice's family represents the inadequate parenting that many of the teens in Coconut Cove seem to have, while Ray's family represents parents who are healthy and engaged enough to provide a positive environment for their child.

Single Variable Calculus, Chapter 7, 7.6, Section 7.6, Problem 66

Evaluate the integral $\displaystyle \int \frac{1}{x \sqrt{x^2-4}} dx$
If we let $\displaystyle u = \frac{2}{x}$, then $\displaystyle x = \frac{2}{u}$ so...
$\displaystyle dx = \frac{-2}{u^2} du$

Thus,

$
\begin{equation}
\begin{aligned}
\int \frac{dx}{x \sqrt{x^2-4}} &= \int \frac{-2 du}{u^2 \left(\frac{2}{u}\right)\sqrt{\left(\frac{2}{u}\right)^2-4}}\\
\\
&= \int \frac{-2 du}{2u \sqrt{\frac{4}{u^2}-4}}\\
\\
&= \int \frac{-2 du}{2u \sqrt{\frac{4-4u^2}{u^2}}}\\
\\
&= \int \frac{-2 du}{2 \sqrt{4-4u^2}}\\
\\
&= -\int \frac{du}{\sqrt{4-4u^2}} = -\int \frac{du}{\sqrt{4(1-u^2)}} = -\int \frac{du}{2\sqrt{1-u^2}}\\
\\
\text{recall that } \frac{d}{dx} \sin^{-1} (x) &= \frac{1}{\sqrt{1-x^2}}\\
\\
&= -\frac{1}{2} \left[ \sin^{-1} u \right] + c \\
\\
&= -\frac{1}{2} \sin^{-1} \left( \frac{2}{x} \right) + c
\end{aligned}
\end{equation}
$

How might I go about structuring a thesis about the corruption of power in Animal Farm?

The most obvious example of power corrupting is the pigs, specifically, Napoleon. Napoleon starts the book with a lot of noble ideals handed down from Old Major. However, as Napoleon begins to enjoy his power and privilege his rule gets more and more tyrannical. He begins enforcing his rule by force with his pack of dogs. He sells Boxer to the glue factory when he is too old to work. He slowly but surely betrays every principle that Animal Farm was based on until, at the end, he is indistinguishable from the humans.
You might also think of more subtle demonstrations and examples of power. For example, Old Major has a great deal of power. The animals all respect him and all of them gather around him early in the book to hear about his vision. The power that love and loyalty to the memory of Old Major keeps the animals true to Animal Farm long after its original ideas begin to fall apart.
The power of intelligence and knowledge in the book quickly becomes the power of manipulation and propaganda. The pigs all use the fact that they are the smartest on the farm to claim special privileges and change the rules. Squealer uses his power to persuade the animals of the success of the farm and the necessity of their sacrifices.
In terms of structuring a thesis, you might think about how power changes or influences different characters. You might also thinks of different types of power (loyalty, love, intellect, strength, and the like). Come up with a main argument about what power does to people, then decide on the different areas you will focus on to prove your point.

y = 2xsinh^-1(2x) - sqrt(1+4x^2) Find the derivative of the function

The expression of this function includes difference, product and two table functions (except the polynomials), sinh^(-1)(z) and sqrt(z).
The difference rule is (u-v)' = u' - v', the product rule is (uv)' = u'v + uv', the chain rule is (u(v(x)))' = u'(v(x))*v'(x).
The derivative of sinh^(-1)(z)  is 1/sqrt(1 + z^2), the derivative of sqrt(z) is 1/(2sqrt(z)).
These rules together give us
y' = 2sinh^-1(2x) + 2x ((2x)')/sqrt(1+(2x)^2) - ((4x^2)')/(2sqrt(1+(2x)^2)) =
= 2sinh^-1(2x) + 2x (2)/sqrt(1+4x^2) - (8x)/(2sqrt(1+4x^2)) =
= 2sinh^-1(2x).