Who are the main characters in the beginning of the story?

Said to be inspired by Nathaniel Hawthorne's "Young Goodman Brown," Stephen King's 1994 short story published in The New Yorker "The Man in the Black Suit" opens with the narrator, Gary, a man in his 90s, preparing to write into his diary a terrifying and vivid memory of an event during his childhood in western Maine.
In the memory from 1914, it is himself at age nine as well as his mother, Loretta, and father, Albion, living on a farm in a sparsely populated rural area. His only brother, Dan, has been dead for a year, killed by a bee sting. He has a Scottie dog named Candy Bill. The only other character who appears in the story is the man in the black suit, who is the incarnation of the devil.

What is a time Crooks feels frustration, anger, relief, loneliness, fear, and humiliation in the book Of Mice and Men?

At the beginning of chapter 4, Lennie enters Crooks's room, which initially upsets and frustrates Crooks. Crooks tells Lennie, "You got no right to come in my room. This here's my room. Nobody got any right in here but me" (Steinbeck, 33). Crooks then begins to bully Lennie by telling him that George might not return. After Lennie becomes extremely angry and threatening, Crooks realizes his mistake and reveals the cause of his pessimistic nature. Crooks laments his difficult situation and reveals his loneliness by saying,

"S'pose you didn't have nobody. S'pose you couldn't go into the bunkhouse and play rummy 'cause you was black. How'd you like that? S'pose you had to sit out here an' read books. Sure you could play horseshoes till it got dark, but then you got to read books. Books ain't no good. A guy needs somebody to be near him . . . A guy goes nuts if he ain't got nobody. Don't make no difference who the guy is, long's he's with you. I tell ya . . . I tell ya a guy gets too lonely an' he gets sick" (Steinbeck, 36).

When Candy enters Crooks's room, he begins talking about their plan to buy their own piece of property and leave the ranch for good. After Candy tells Crooks that they already have the money, Crooks experiences a feeling of relief and hope in the possibility that he might be able to join the men. Crooks tells Candy,

"If you . . . guys would want a hand to work for nothing—just his keep, why I'd come an' lend a hand. I ain't so crippled I can't work like a son-of-a-bitch if I want to" (Steinbeck, 37).

Curley's wife then enters Crooks's room and laughs after hearing about their dream of one day leaving the ranch. After she begins messing with Lennie, Crooks displays his anger and frustration by saying,

"I had enough . . . You got no rights comin' in a colored man's room. You got no rights messing around in here at all. Now you jus' get out, an' get out quick. If you don't, I'm gonna ast the boss not to ever let you come in the barn no more" (Steinbeck, 39).

Immediately after being chastised, Curley's wife threatens to have Crooks lynched. Crooks becomes helpless, afraid, and humiliated by Curley's wife. Steinbeck writes,

Crooks had reduced himself to nothing. There was no personality, no ego—nothing to arouse either like or dislike. He said, "Yes, ma'am," and his voice was toneless (39).

College Algebra, Chapter 5, Review Exercise, Section Review Exercise, Problem 18

Determine the domain of the function $g(x) = \log (2 + x - x^2)$
If the given is a Logarithmic Function, then we want

$
\begin{equation}
\begin{aligned}
2 + x - x^2 &> 0 && \text{Model}\\
\\
x^2 - x - 2 &< 0 && \text{Multiply both sides by } -1\\
\\
(x+1)(x-2) &< 0 && \text{Factor}
\end{aligned}
\end{equation}
$

The factors on the left hand side are $x + 1$ and $x - 2$, these factors are 0 when $x$ is $-1$ and $2$ respectively. These numbers divide the number line
into intervals
$(-\infty,-1)(-1,2)(2,\infty)$
By testing some points in the interval,


Thus $(x + 1)(x-2) < 0$ at interval $(-1,2)$. Therefore, the domain of $g$ is $(-1,2)$

What do you admire or dislike about Rainsford?

While Rainsford may be foolish to go so near the side of the boat (an event that causes his fall into the water and eventual capture by Zaroff), there are quite a number of things about Rainsford in Connell's "The Most Dangerous Game" that make this world-renowned hunter admirable.
Perhaps what I admire most is that even though Rainsford loves to hunt, he has no desire to compromise his moral code by hunting humans. Even though he is on an island under circumstances that would never allow anyone to know if he were to join Zaroff, it never occurs to him. His integrity is not governed by whether or not someone is watching, but by his unshakable sense of what he knows to be right.

“Tonight,” said the general, “we will hunt—you and I.”
Rainsford shook his head. “No, general,” he said. “I will not hunt.”

Another thing that I admire about Rainsford is his ability to think creatively even while running for his life. While running, he is able to come up with unusual methods not only to protect himself (like climbing the tree), he also adopts methods of defense to remove threats against him (such as Ivan) and engages in unique offensive tactics.

“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."

Finally, though Rainsford initially experiences a moment of panic, he is able to work past it to do whatever he can to protect himself and survive.
Ironically, while Zaroff looks to find the "most dangerous game" in capturing and hunting unfortunate sailors, Rainsford's abilities to adapt and strategize make him the most dangerous game.

What does the mother compare her life to?

In "Mother to Son", the mother compares her life to a splintered and dilapidated stairway:


It’s had tacks in it,
And splinters,
And boards torn up

A stairway is a means of getting somewhere or, literally, of moving up in the world. So, the mother could be comparing her life here, metaphorically, to a splintered and dilapidated stairway to suggest that her path in life has been a difficult one. The "tacks" and "splinters" and the ripped up "boards" could represent the obstacles that she has had to overcome. The description of the stairway also implies poverty, especially when compounded with the word "Bare" two lines later, so perhaps the mother's life has been difficult because she has been poor, and the obstacles that she has had to overcome are the obstacles that poverty imposes.

The speaker (the mother) then continues the metaphor and says that, on the "landin's" and while "turnin' corners," she has had nobody else to guide her. She has had to find her own way. This is implied by the lines,


And sometimes goin’ in the dark
Where there ain’t been no light.

The absence of light here could suggest that she has had nobody to guide her, as a light might guide somebody through the darkness. She has had to turn corners in her life, and find doorways in her life, without the guidance that most might expect somewhere along the way.

The mother compares her life to a staircase filled with nails, broken boards, and missing boards. For her, life has not been easy. She sees her life as a struggle upwards, fighting against injustice, discrimination, and despair. In the poem, she states "I'se been a-climbin' on, / And reachin' landin's, / And turnin' corners, / And sometimes goin' in the dark / Where there ain't been no light." She has been met with dead-ends, anxiety, and the unknown. However, even with all of this struggle and pain, she keeps going, because that's all she knows how to do. To keep going in the face of all of this shows her strength of character and her belief that if she just keeps climbing, life will be better for her and her son. She tells him, "So, boy, don't you turn back. / Don't you set down on the steps. / 'Cause you finds / it's kinder hard. / Don't you fall now— / For I'se still goin', honey, / I'se still climbin'" and extends the metaphor of the stair and her life to show her son that she can still keep going and he can, too.

Who is called the Queen of Courtesy in the poem "Pearl" and why?

In the Middle English in which the poem was written, cortayse has much broader connotations than the modern-day "courtesy." The word is related to "court," as in a royal court, and in the context of the poem represents the very highest nobility, dignity, graciousness, and benevolence. All of these qualities and more are exemplified by the Queen of Courtesy, the Virgin Mary herself.
But courtesy is much more than good manners; it is the grace of God Himself. According to Medieval Christian theology, the Virgin Mary, in her capacity as the Queen of Courtesy, is instrumental in the distribution of God's grace. Through her, this most wondrous of heavenly gifts is bestowed. The grieving father's deceased daughter is the recipient of such gifts; she has become part of the community of grace. The child's gift of grace was entirely undeserved, as was her father's tragic loss.

Identify and explain an overarching theme found in Roger Williams's work.

An overarching theme in Roger Williams's work is religious freedom. He wrote about this in several works, including his famous The Bloudy Tenent of Persecution, for Cause of Conscience and his work The Bloudy Tenent Yet More Bloudy.
In Bloudy Tenent of Persecution, written in 1644, Williams calls for the separation of church and state, using the Bible to support his argument. He argued for the religious freedom of the various Protestant sects and argued for Catholics, Jews, Muslims and other "heretical" groups to be left free to worship as they wished. He based this assertion of religious freedom on Jesus's teaching that God would ultimately judge who was and was not righteous. If the state judged and persecuted people for their faith, the state usurped God's role. The state could, through poor decisions, harm the good "wheat" of the truly faithful followers of Christ.
Williams stated that the Bible condemned kings like Nebuchadnezzar who forced Jews to worship the gods of the state against their conscience. He quoted Paul to argue that the state should use only spiritual, not physical, weapons to convince unbelievers. Williams also thought the beast in Revelation was the symbol of state churches.
Williams wrote:
It is the will and command of God that, since the coming of his Son the Lord Jesus, a permission of the most Paganish, Jewish, Turkish, or anti-christian consciences and worships be granted to all men in all nations and countries : and they are only to be fought against with that sword which is only, in soul matters, able to conquer: to wit, the sword of God's Spirit, the word of God.
After he was attacked for arguing in favor of the separation of church and state, he repeated and elaborated on his arguments in The Bloudy Tenent Yet More Bloudy.
His arguments for religious freedom clearly found favor in the the United States, where freedom of religion was enshrined in the Constitution. Nevertheless, his ideas were radical for a time when church and state were tightly tied together and when the monarch was considered God's representative on earth.