What is Madam Lockton like?

I'll start with something fairly tame. Madam Lockton is a wealthy woman who is also a British Loyalist. That's about the nicest thing that readers can say about her.
She's a slave owner, unkind and unfair. She makes it her personal goal to find ways to hurt Isabel. Madam Lockton is also fully capable of hurting Isabel in both physical and emotional ways. At one point in the story, Madam Lockton gives a severe beating to Isabel, who bravely takes the beating in Ruth's place. Later, Madam Lockton has Isabel branded on the face with the letter "I" for insolence. To hurt Isabel emotionally, Madam Lockton lies to Isabel and tells her that Ruth has been sold to another owner. Chapter 43 has a great quote that shows what Isabel thinks of Madam Lockton.

Everybody carried a little evil in them, Momma once told me. Madam Lockton had more than her share. The poison had eaten holes through her soul and made room for vermin to nest inside her.

Madam Lockton is a greedy and selfish woman, and she takes out her anger and frustrations on other people. This occasionally comes back at her in bad ways. Her actions feed her husband's temper, and he is a violent man himself. Often their fights become physical, but Madam Lockton is so rotten to the core that it is nearly impossible to feel any sympathy toward her.

What message does the poem "Dover Beach" give you?

Montag decides to risk revealing that he has a book in order to share a poem first with Mildred, his wife, and then later with her and some of her friends who are visitors in their home. He chooses a serious poem about love, responsibility, and war, intending to shake them out of their passive reverie. Although he knows his behavior is reckless, he has reached the point of no return in regard to participating in his society's repression and hypocrisy.
"Dover Beach" begins with an appeal to love and fidelity, which Montag is about to reject as he places his wife in danger: "Ah, love, let us be true/To one another!"
The poem is appropriate, nonetheless, in calling attention to the illusory nature of reality, which Montag is grappling with every day:

...the world... seemsTo lie before us like a land of dreams,So various, so beautiful, so new....

Montag has come to believe that humanity's dark side is controlling society, so the poem's message of the absence of joy and light, suits his newfound understanding.
They live in a world perennially on the brink of war but are discouraged from facing that. The distractions such as wall TV are no longer enough for Montag; there is no "help for pain...."
He identifies with the internal battles of the poem's characters, who are "Swept with confused alarms of struggle and flight," and he is at the point of rejecting the "ignorant armies [that] clash by night."
Montag is a romantic by nature, who wants to believe that being true and love are important in life, and this poem, amidst its bleakness, is giving him courage to move past his confusion and join in "struggle and flight."
https://poets.org/poem/dover-beach

At the end of part two, Montag leaves Faber's house and travels home to find Mildred and her friends watching the parlor wall televisions. Montag, who is furious with society, attempts to shock the superficial women by reading them poetry. When Mildred suggests that Montag read a "funny" poem, Montag reads "Dover Beach." The poem gives a pessimistic description of a faithless world, void of spirituality, hope, justice, and wisdom, which correlates with Bradbury's dystopian society throughout the novel. Matthew Arnold, the poem's author, depicts a dismal world, caught up in "confused alarms of struggle and flight," without any hope for beauty and tranquility in life. The message of the poem is meant to give the reader insight into the emptiness of humanity. Arnold's description of modern society is a bleak depiction of humanity's corrupted nature. The negative images and disturbing message have a dramatic impact on Mrs. Phelps, who begins to cry. She can relate to the empty images throughout the poem, which describe her superficial, sad life.

Calculus of a Single Variable, Chapter 6, 6.4, Section 6.4, Problem 10

(y-1)sin(x)dx - dy = 0
To solve, express the equation in the form N(y)dy = M(x)dx.
So bringing same variables on one side, the equation becomes:
(y-1) sin(x) dx = dy
sin(x) dx = dy/(y - 1)
Then, take the integral of both sides.
int sin(x) dx = int dy/(y-1)
For the left side, apply the formula int sin (u) du = -cos(u) + C .
And for the right side, apply the formula int (du)/u =ln|u| + C .
-cos(x) +C_1 = ln|y-1|+C_2
From here, isolate the y.
-cos(x) + C_1 - C_2 = ln|y-1|
Since C1 and C2 represent any number, express it as a single constant C.
-cos(x) +C = ln|y-1|
Then, eliminate the logarithm in the equation.
e^(-cos(x)+C) = e^(ln|y-1|)
e^(-cos(x) + C) = |y-1|
+-e^(-cos(x) + C) = y-1
To simplify the left side, apply the exponent rule a^m*a^n=a^(m+n) .
+-e^(-cos(x))*e^C= y-1
+-e^C*e^(-cos(x))=y-1
Since +-e^C is a constant, it can be replaced with C.
Ce^(-cos(x))=y - 1
Ce^(-cos(x))+1=y
Therefore, the general solution is y=Ce^(-cos(x))+1 .

Why is water a good negative control for chemical tests?

A control is used, in any experimentation, to check whether the obtained result is due to the test variable (a condition that is varied) or not. Both the positive and the negative controls are used for this purpose. A positive control allows us to assess the validity of the test. In other words, a positive control is an experiment where we test against something that we know works. In comparison, a negative control is an experiment that gives negative response or no response.
Any substance can be used as a negative control if we know that it will not interfere with the test or will not participate in it.
Water is commonly used as a negative control in chemical tests, especially distilled water. The distilled water is devoid of any minerals or salts, unlike regular water (or tap water) and hence is not likely to participate in any chemical reaction. This property makes it an ideal choice as a negative control in a number of chemical tests.
Another way to think about it is to consider that distilled water has only water molecules and has consistent properties. Due to this reason, it is safe to assume that any experimental observation is due to the change in the variable under study and not the addition of water.
Hope this helps.

You were presented with the option to finance a home for 15 years or 20 years. Would you expect to have the same interest rate on either mortgage or would one of them have a lower interest rate?

When considering mortgage rates, there is no reason to rely on intuition or expectations when one can easily do research to discover what the actual rates are. Currently, as of June 2018, a fixed rate mortgage with a 15-year term has a lower interest rate than a 20-year mortgage, with 30-year mortgages having even higher rates than both of the shorter-term options. As a consumer, though, one should be aware that the difference in terms of the loans means that over the lifetime of a loan, even if interest rates are equal, one ends up paying considerably less interest on a shorter-term loan, and so, despite the higher monthly payments, shorter-term loans are the best financial choice, assuming one can afford the payments.
The reason for this difference is that lenders carry risk for a longer time in the case of longer-term loans, something that is reflected in the higher interest rates.

In physics, what is defined as the product of an object's mass and velocity?

The product of an object's mass and velocity
   P=mv
Momentum = p
Velocity = v
Are vector quantity
Vector quantity meaning they have mangitute and direction.
The unit of momentum are  kg* m/s

The product of mass and velocity is momentum.  
A good way to summarize momentum is to say momentum is mass in motion. All objects have mass, but not all objects are moving; therefore, not all objects have momentum. If an object is moving, though, it has momentum. Because the equation for momentum involves multiplication, increases in either mass or velocity will result in the increase of momentum. That means a football linebacker can increase his hitting power by gaining mass, becoming faster, or both. 
Some students occasionally confuse momentum and inertia. All objects always have inertia because inertia depends only on mass. Inertia is a resistance to changes in any motion. An object will have the exact same inertia whether it is moving or not, but an object will have zero momentum if it is stationary. That particular object's momentum will increase as it begins to increase its velocity. 

In The Merchant of Venice, why does Launcelot want to leave Shylock's service?

At the beginning of scene 2, Act II, Launcelot mentions one of the reasons why he should leave Shylock's service. In his monologue, he makes it clear that it is not an easy decision and is something that sits on his conscience. He believes, however, that Shylock 'is a kind of devil' and later emphasizes this by stating that 'the Jew is the very devil incarnal,' when he actually means incarnate. The implication is that Shylock is very difficult person to work for since he makes Launcelot's life a misery. Launcelot resolves that he will follow the advice of the fiendish aspect of his conscience and run away.
Later in the scene he provides another reason for his desire to abandon his employer. In conversation with his father, Launcelot Gobbo, who wishes to present a gift to Shylock, he states the following:

My master's a very Jew: givehim a present! give him a halter: I am famished inhis service; you may tell every finger I have withmy ribs.

The reference to 'a very Jew' in this instance, has a derogatory connotation since it suggests that Shylock is stingy. His statement clearly reveals a stereotypical and cynical perception of Jews. Launcelot states that Shylock does not feed him properly since he is famished and has grown so thin that his ribs are as clearly discernible as his fingers. He wishes to be in Bassanio's service because he will provide him with 'rare new liveries.' This furthermore suggests that Shylock has not clothed him suitably and has deliberately not provided him with a new outfit for quite some time.
Later in the scene, when Launcelot tells Bassanio about his plans, he also mentions that he would prefer being in his service since Bassanio has the 'grace of God' whilst Shylock has only enough. The implication is obvious: Bassanio has more than enough generosity and kindness to give to everyone, whilst Shylock's is just enough for himself - he has nothing left to share.
If one considers all Launcelot mentions, it becomes quite understandable why he is so desperate to leave.
It is quite ironic, though, that Shylock later, in scene V, tells Launcelot that he will not have the opportunity to greedily stuff himself as full of food when in Bassanio's employ as he had been whilst working for him.