What is the role of genealogy in The Children of Men?

The Children of Men by P.D. James is a dystopian novel that depicts a world where all men are infertile and mankind is on the brink of extinction. Since the survival of the human race depends on a child being born, there is a desire for any possible children to be bred from the healthiest and strongest men and women possible. Because of this, there is a need for identifying citizens whose genealogies reveal strong and healthy families. Qualifying men and women are given compulsory fertility tests, while unhealthy or disabled people are excluded. 
Besides this very pragmatic need, genealogy seems to be surprisingly unimportant in The Children of Men. Since there is no chance of continuing, the family unit has almost disintegrated. Sex is no longer used for procreation. The elderly are murdered in state-sanctioned rituals called the "Quietus." People live for the pleasure of the moment in order to defend themselves against the grief of childlessness and their coming extinction. 
Even British aristocrats, who are typically notorious for being proud of their rich heritage, care little now for the land and manors they have inherited from their ancestors. Theo explains this phenomenon in the following passage:

I can understand how the aristocrats and great landowners with no hope of posterity leave their estates untended. We can experience nothing but the present moment, live in no other second of time, and to understand this is as close as we can get to eternal life.

It seems that the need to appreciate the past is dependent on humanity's ability to appreciate the future. Without a coming generation to carry on the family history, the genealogy of these citizens is forgotten. Only the present is valued.

What is the citation in MLA style for this story?

The citation for Jack London's story "To Build a Fire" in MLA (Modern Language Association) style (8th edition) depends upon how you accessed the work. If you accessed it through an anthology or a textbook that contains multiple stories, you would cite the anthology or textbook as the "container" of the work. However, if you accessed the work online, then you would cite the website as the "container" and give the URL and date accessed.
One anthology that contains London's story is the Norton Anthology of American Literature. The Works Cited citation for the story found in that book is as follows:
London, Jack. "To Build a Fire." Norton Anthology of American Literature, edited by Nina Baym, 8th ed., vol. E, W. W. Norton, 2012, pp. 1047 - 1058.
The in-text parenthetical citation would be: (London 1047) or whatever specific page you are quoting or paraphrasing from.
You can access the story online in many places since its copyright protection has expired. One site that features the entire story is the Library of America's Story of the Week. Here is how that works cited citation would look:
London, Jack. "To Build a Fire." Story of the Week, Literary Classics of the United States Inc., 25 Feb. 2011, http://storyoftheweek.loa.org/2011/02/to-build-fire.html. Accessed 8 Feb. 2018.
You would use the day that you look it up online as the "accessed" date. Since the website does not have page numbers, your in-text parenthetical would not need a page number. It would just need the author's name (like this): (London).
You must adapt your citation to reflect the actual source that you used to read the story. The above examples show the difference between a print and online citation in the MLA Style 8th edition.
https://style.mla.org/works-cited-a-quick-guide-book/

What happened to the community in Gathering Blue?

Gathering Blue depicts a post-apocalyptic society. The exact form the apocalypse took remains cryptic in the novel, but as the story begins, the "civilization of the ancestors" had ended long ago. The society is now primitive, operating without any technology to speak of, and most people in the society are illiterate. The method they have for retaining their history is oral: A Singer presents a Ruin Song annually to the entire community which tells the history of people. The part of the Ruin Song that refers to the apocalypse speaks of "smoky, poisonous fumes, of great fractures in the earth itself, of the way huge buildings toppled and were swept away by the seas." The Singer's robe depicts through embroidery the scenes mentioned in the Song. Kira repairs an area of the robe that shows "tall buildings ... against a background of fiery explosions." These were skyscrapers, destroyed in a war.
The words to accompany that section of the robe say, "Burn, scourged world / Furious furnace, / Inferno impure." That the destruction was widespread, even worldwide, is implied by the verse, "Ravaged all, / Bogo tabal / Timore toron / Totoo now gone." Destruction ranged from Bogata to Baltimore to Toronto, meaning that cities on both the North and South American continents were destroyed. The fact that many humans are physically deformed in the village where Christopher lives suggests either nuclear or chemical weapons were used that caused congenital defects for generations.
Though Lowry never specifically says so, one assumes that a World War, including nuclear weapons, wiped out civilization as we know it. Kira's community rebuilt, but without technology and without many of the markers that define our culture, such as religion, education, philosophy, and the arts.

What are the two opposite attitudes toward tradition in the poem "Mending Wall" by Robert Frost?

For the narrator, tradition by itself is unimportant. In his case, it creates unnecessary work that serves no good purpose. For his neighbor, tradition is all-important and must be adhered to for tradition's sake.
The tradition in question is the annual mending of the stone wall between the two men's properties. Every year, the two meet for the laborious process of repairing gaps in the wall.
The narrator thinks it is ridiculous to worry about mending the wall, as neither of them keeps livestock that could damage the other one's crops. The speaker grows apple trees and the neighbor pines: they don't need a wall.
The neighbor, however, learned from his father the saying that "good fences make good neighbors" and doesn't question the truth or logic of that statement. The narrator does, asking himself, "why do they [fences] make good neighbors?"
The neighbor likes to repeat his father's motto and derives satisfaction from keeping up his father's traditions. The narrator wants to break with these traditions because they don't make sense to him.

In Robert Frost's "Mending Wall," the speaker and the speaker's neighbor meet each year to mend a stone wall that separates their properties. Through the speaker, the reader learns the annual maintenance is, in the speaker’s mind, unnecessary because the wall does not serve a practical purpose. The speaker also reveals the annual tradition of mending the wall is important to the neighbor not for the wall itself, but for what the neighbor believes the wall represents.
The speaker's attitude toward this annual tradition seems to range from bemusement to irreverence. The speaker questions not only the purpose of the shared annual labor, but also the neighbor's rationale for continuing the tradition in the face of the lack of practical need for the wall's continued existence. The speaker wants to make light of the tradition, even pondering suggesting that elves are responsible for the yearly damage to the wall, but in the end acquiesces to the neighbor’s determination to follow the tradition.   
The speaker's neighbor, on the other hand, does not seem to question the tradition. Rather, the neighbor dogmatically follows the platitude, “Good fences make good neighbors,” a saying the speaker attributes to the neighbor’s father. For the neighbor, the wall and the annual mending both represent traditions to be followed for their own sake, not for their practical purposes. Further, the tradition of annually mending the wall seems to represent to the neighbor a necessary tradition for maintaining their relationship as neighbors.

Why do you think Mrs. Jones makes a point of getting Roger to wash his face? Why does she give him food? Why does she tell him about her past? Why does she avoid asking him about his family or background?

After Roger tells Mrs. Jones that he tried to steal her purse to get money to buy blue suede shoes, Mrs. Jones begins to talk to Roger about her past; Roger is so surprised by her honesty that he cannot come up with words:

“'Well, you didn’t have to snatch my pocketbook to get some suede shoes,' said Mrs. Luella Bates Washington Jones. 'You could of asked me' 'M’am?' The water dripping from his face, the boy looked at her.There was a long pause. A very long pause. After he had dried his face and not knowing what else to do dried it again, the boy turned around, wondering what next. The door was open. He could make a dash for it down the hall. He could run, run, run, run, run! The woman was sitting on the day-bed. After a while she said, 'I were young once and I wanted things I could not get.' There was another long pause. The boy’s mouth opened. Then he frowned, but not knowing he frowned"

This conversation likely feels awkward and uncomfortable to Roger; he cannot come up with words and contemplates running away. There is more than one "long pause" and Roger is left frowning, open mouthed (suggestive of surprise or discomfort) at the end of the paragraph. 
Throughout their conversation, Mrs. Jones shows concern for Roger's well-being. She wants to make sure he is clean and well-fed so that he can be comfortable while they talk. She worries that his needs may not be met at home, as seen when she asks him if he has eaten. In the paragraph above, there is evidence that Mrs. Jones has some familiarity with poverty: "I were young once," she says, "and I wanted things I could not get." Her past experience with poverty increases her sympathy for this poor, dirty, and hungry boy who tried to steal her purse.
Just after the passage above, Mrs. Jones continues to talk to Roger:

"'Um-hum! You thought I was going to say but, didn’t you? You thought I was 3 going to say, but I didn’t snatch people’s pocketbooks. Well, I wasn’t going to say that.' Pause. Silence. 'I have done things, too, which I would not tell you, son—neither tell God, if he didn’t already know. So you set down while I fix us something to eat. You might run that comb through your hair so you will look presentable.'"

Here, we discover more information about why Mrs. Jones is concerned with Roger's appearance. She's not only concerned with his comfort; she's also trying to show him how to make himself look socially "presentable," so he can make a create a positive impression through his physical appearance. Mrs. Jones does not explain how she came out of her hard times, but she admits that she had challenges with money growing up. Now, she is able to buy food, pay for some household comforts (such as clean towels and warm water), and share her money with people who need it. This is seen when she tells Roger he only needed to ask, rather than trying to steal from her. It's also seen when she gives him the gift of $10 for his blue suede shoes at the end of the story. She takes care of herself, keeping herself clean and working hard to meet her daily needs. She encourages Roger to do the same thing and to get what he wants through respectable methods, such as asking people and working hard, rather than through stealing and crime.
Why does Mrs. Jones not ask Roger about his family? We can't know for sure, but we can make thoughtful assumptions. Perhaps she does not want to make him feel even more uncomfortable. We know he is uncomfortable since he is thinking about running away from the house. Perhaps she knows that a conversation about his hard circumstances might make him feel judged or attacked. Perhaps she can already guess what his childhood is like due to her own hard childhood experiences. Or, perhaps she is waiting for Roger to direct their conversation. Maybe she would be interested in talking about his family life if he brought the topic up. Since he's being so quiet, she probably assumes he does not want to talk right now.

360 square tiles of length 30cm were needed to cover the floor of a room which is 7 m 20 cm long. If no tiles were cut , find the width of the room.

We are given that 360 tiles were required to tile a floor: the tiles are square and 30 cm on edge. The length of the room is 7m 20cm, and we are asked to determine the width of the room assuming that no tiles were required to be cut.
The area of the room can be found by multiplying the length by the width.
A=lw
Converting all units to the same unit, here we choose cm, we get:
A=324000 square centimeters (360 times the area of each tile or 360*900 square centimeters.)
l=7m20cm=720cm
The width can be found by dividing the area by the length:
w=(324000 "cm"^2)/(720"cm")=450"cm"
 

How important is A Passion in the Desert?

The "importance" of a literary work is not something one can measure in a simple objective fashion. Instead, works of literature can be important to specific people or scholars or with certain contexts for various different reasons.
"A Passion In The Desert" (Une Passion Dans Le Désert) by Honoré de Balzac was a short story originally published in the December 1830 issue of a small literary magazine Revue de Paris and later incorporated into other larger collections of works by Balzac. It was originally translated into English by the important "decadent" poet Ernest Dowson and in 1998 made into a film by director Lavinia Currier.
French novelist and playwright Honoré de Balzac (1799-1850) is widely considered an important figure in the development of realistic fiction in the nineteenth century and is normally read by all students studying French literature. He is important within the history of European fiction and the history of nineteenth-century literature.
"A Passion In The Desert" is not one of the best known or most influential works by Balzac, but was popular in its own period due to its addressing a topic very important in the French and European imagination, the Napoleonic wars in Egypt. Modern scholars interested in colonialism and the relationship between people and animals in literature are particularly interested in this work.
Eugénie Grandet and Le Père Goriot are probably the best known works by Balzac, but he was an extremely prolific writer and many of his works continue to be read and studied by a wide range of readers, students, and scholars.