O’Connor characterizes the children as being obnoxious. What is the significance of this choice? Would the result of the story be different if she characterized them in another way?

In "A Good Man is Hard to Find" by Flannery O'Connor, the author portrays the children as obnoxious in a way that fits in with the "meanness" of rest of the characters. Lack of kindness is a large theme within the story, so much so that when The Misfit's two associates kill the entire family, the reader is left without much sadness from the event.
One of the biggest clues to O'Connor's portrayal of John Wesley and June Star comes not from the children themselves, but rather from The Misfit's speech about Jesus:

"Jesus was the only One that ever raised the dead," The Misfit continued, "and He shouldn't have done it. He thrown everything off balance. If he did what He said, then it's nothing for you to do but throw away everything and follow Him, and if He didn't, then it's nothing for you to do but enjoy the few minutes you got left the best way you can by killing somebody or burning down his house or doing some other meanness to him. No pleasure but meanness," he said and his voice had become almost a snarl.

On the surface, this is a morally ambiguous justification for murder. However, upon deeper reflection, this passage also acts as a commentary on the state of relationships and interaction in society. "No pleasure but meanness" represents nearly every character's attitude toward others throughout the story. The children are disrespectful to their grandmother; Red Sammy is distrustful of everyone and treats his wife poorly; Bailey ignores and has a short temper with his family; and the grandmother herself acts as a "better than everyone" know-it-all. In the most telling line of the story, the grandmother—after listening to Red Sammy talk about not knowing who to trust anymore—says, "[p]eople are certainly not nice like they used to be." This overarching theme of "meanness" plays out in a way that makes it hard to sympathize with any of the characters.
Early in the story, the two children respond to their grandmother's suggestion of traveling to east Tennessee (rather than Florida) with contempt. "If you don't want to go to Florida, why dontcha stay at home," quips John Wesley, while June Star responds, "She wouldn't stay at home to be queen for a day." While this shows their level of disrespect, the lack of response from their parents further adds to the "meanness" theme in the story. Though the grandmother does not act much better, by the end of the story the reader is left to wonder how differently it might have turned out had the family taken her "east Tennessee" suggestion more seriously.
When the family visits Red Sammy's diner, the children are again portrayed as obnoxious. After June Star's dancing is complemented by Red Sammy's wife, she responds by saying she "wouldn't live in a broken-down place like this for a million bucks!" Later, when Bailey initially refuses the children's request to visit a house with a secret panel, the children "yell and scream" in order to get their way. Finally, after the car accident, they "screamed in a frenzy of delight," despite their screaming baby brother and injured mother.
In short, the obnoxious characterization of John Wesley and June Star fits in with the story's theme of "meanness." They disrespect their grandmother, throw tantrums to get their way, and appear to find delight in a potentially deadly car crash. By the time The Misfit shows up, the children—as well as the rest of the family—are so insufferable that none of their deaths evoke a strong emotional response from the reader. The one exception is the baby, though one can imagine him growing up to be just as dreadful as the rest of the family.

Compare and contrast Joe and Mrs. Joe Gargery in terms of looks and behavior.

Joe has curly "flaxen" hair (which means it is pale blond), a smooth face, and blue eyes. He is the kindest of men. Pip describes him as mild-mannered, easy-going, flexible, "foolish," and a "dear."
Mrs. Joe is the opposite of Joe in both looks and behavior. She has black hair and coarse red skin. Pip sometimes wonders if she doesn't wash herself with a nutmeg grater rather than soap. She is tall and lean. She wears an apron with a square bib that is always stuck with pins. Pip records that she hits both Joe and himself. As Pip puts, Mrs. Joe has

a hard and heavy hand, and . . . [is] much in the habit of laying it upon her husband as well as upon me . . .

Mrs. Joe is a harsh, bad-tempered woman who makes it clear that Pip is a burden to her even though he is her own brother. Joe, in contrast, though he is only related to Pip through marriage, genuinely cares for the boy and treats him with gentleness and compassion.

What mood or feeling is created by the images Edwards uses in his sermon?

One of the first images that Edwards uses in the sermon is that of a person whose foot slides, causing the person to fall down. This is not only a visual (and perhaps even tactile) image, but it is also a powerful metaphor. He says that people who do not accept God into their lives or remain faithful are taking a similar risk as a person who walks on ice. Just as that person is liable, at some point, to fall down, those individuals who, "notwithstanding all God's wonderful works towards them, [remain] void of counsel, have no understanding in them," take a far worse risk: they are already on the figurative ice and, when God's appointed time comes, he will allow them to be cast down. He will not hold them up from on that figurative ice any longer. Such an image, of being allowed to slip and fall (as one would be cast down into hell) creates a mood of fear. Edwards wants to compel his listeners to change, and fear is a powerful motivator for change.
Soon after, Edwards employs more images designed to create a similar mood. He says,

Though hand join in hand, and vast multitudes of God's enemies combine and associate themselves, they are easily broken in pieces. They are as great heaps of light chaff before the whirlwind; or large quantities of dry stubble before devouring flames. We find it easy to tread on and crush a worm that we see crawling on the earth; so it is easy for us to cut or singe a slender thread that any thing hangs by: thus easy is it for God, when he pleases, to cast his enemies down to hell.

We have an image, first, of those who oppose God being compared, via simile, to dry corn husks or hay being whipped about by the winds or even being quickly consumed by fire. Next, we have the lowly worm or a single thread, coupled with the idea that it is as easy for God to cast one to hell as it is for us to crush that worm or snip that thread. Again, these images create fear in listeners, fear meant to compel them to change their ways.

How does Athena get Telemachus to hurry home from Menelaus's estate?

This question is in reference to the events of book 15. It opens late at night, in Sparta, as Telemachus is struggling to fall asleep (at least, this is the suggestion in the Fagles translation). In this situation, Athena stands over him, ready to spur him to depart. She says that in traveling so far from home, he has left his holdings vulnerable, at the hands of those who would "carve up all your wealth, devour it all, / and then your journey here will come to nothing" (The Odyssey, trans. Robert Fagles, Penguin Classics (paperback ed.): New York, 1996, 319). Therefore, she insists that he get Menelaus to let him leave immediately, as Penelope is already being pressured to wed Eurymachus, whose gifts exceed those of any other Suitor.
At the same time, she warns him about the ambush the Suitors have planned against him and gives him instructions for avoiding it. With that, she departs for Olympus. The next morning, Telemachus will again meet with his hosts and, later still, set off on his journey back to Ithaca.

On a day with no wind, a hot air balloon hovers at a point abouve a long, straight river. On the west side of the balloon, a sailboat is spotted in the river at an angle of depression of 48 degrees. On the east side, a canoe spots the balloon at an angle of inclination of 29 degrees. The distance between the balloon and the canoe is 650 m. a) What is the height of the balloon? b) What is the distance between the balloon and the sailboat? c) What is the distance between the sailboat and the canoe?

The given question can be represented as a figure as shown in the attachment.
Let h be the height of the balloon above the river.
x be the distance of the balloon from the sailboat and y be the distance between the sail boat and the canoe where y=s+t (from the figure).
Given that the distance between the balloon and the canoe is 650m.
Now we know that,
sin\theta=\frac{Opposite\ side}{Hypotenuse}
So we can write,
sin29^0=\frac{h}{650}
i.e.
h=650sin29^0=650\times 0.4848=315.12\ m
Now similarly,
sin48^0=\frac{h}{x}
i.e.
x=\frac{h}{sin48^0}=\frac{315.12}{0.7431}=424.06\ m
Now we know that,
tan\theta=\frac{Opposite\ side}{Adjacent \ side}
So we can write,
tan48^0=\frac{h}{s}=\frac{315.12}{s}
i.e.
s=\frac{315.12}{tan48^0}=\frac{315.12}{1.111}= 283.64\ m
And,
tan29^0=\frac{h}{t}=\frac{315.12}{t}
i.e.
t=\frac{315.12}{tan29^0}=\frac{315.12}{0.5543}=568.50\ m
Finally,
y=s+t=283.64+568.50=852.14\ m
Hence we have the answers as:
a) Height of the balloon = h = 315.12 m
b) Distance between the balloon and the sailboat = x = 424.06 m
c) Distance between the sailboat and the canoe = y = 852.14 m

Why did you choose this book?

Based on your question, I'm assuming that you were given a choice on what to read, and you've chosen Kim by Rudyard Kipling. Therefore, your answer should be personal, and you need to consider specifically why you've chosen to read this book.
Kipling's Kim is an adventure/coming-of-age novel about an Irish orphan growing up in British-occupied India in the 1880s and 1890s. The story centers around the boy's adventures as he meets people from many different backgrounds and religions, from Buddhist lamas to undercover agents during a conflict between the Russians and the British. So, now you need to ask yourself what about this story makes you interested in reading it. Consider these questions to get started:
Do you like stories with adventure and suspense?
Do you like to learn about different cultures, languages, and religions and how they interact (i.e., Buddhism, Islam, Hinduism, Christianity)?
Do you want to learn about the history and geography of India?
Do you like stories in which the main character is a young person like yourself who has to go on a secret quest?
Do you want to know what it's like to be an orphan in an unknown place?
Good luck, and I hope you enjoy answering a question that is really about your own interests and connections to this book!

What is promotional literature related to John Smith's "The General History of Virginia, New England, and the Summer Isles"?

Promotional literature, in this case, means literature intended to promote a commercial venture. The first permanent English settlement in America was sponsored by a private joint-stock company: the London Company of Virginia.
This company received its official charter from King James I in 1606, sold shares to the public, and used the pooled capital to outfit ships and supplies for the proposed English colonies in North America. In Renaissance England, wealthy London merchants (and members of the nobility) were interested in investing their capital in foreign trading ventures.
The company selected Sir Thomas Smythe, a wealthy merchant and former governor of the British East India Company, to lead the Virginia Company. Because the national honor, the reputations, and the fortunes of many high-profile investors (including the king and leading nobility) were at stake, the company was granted certain privileges to protect its interests. One of these privileges was that all printed materials about the venture were to be approved by the company before publication. That way any inconvenient information that would tend to discourage investment or settlement could be handled with care or simply edited out.
It appears that this is what happened with Sir John Smith's "The General History of Virginia, New England, and the Somers Isles" because in addition to being history, it was also intended to promote further sales of stock in the company. For this reason, the merits of the settlement were likely emphasized, while the negatives tended to be downplayed.