In what ways are friendship and trust demonstrated throughout the novel To Kill a Mockingbird?

Friendship and trust are explored in the novel through various character's interactions with one another during particularly adverse situations. Miss Maudie displays her friendship and trust by supporting the Finch family before and after the controversial trial of Tom Robinson. She is quick to encourage Jem following the trial and stands up for Atticus' decision to defend Tom during the missionary circle. Jem and Scout's relationship with Dill also demonstrates friendship and trust. They not only play together but also get themselves into several precarious situations. The three children trust each other and stick up for one another whenever threatened with punishment. Jem is quick to deny the fact that they are acting out Boo's life story, and Dill lies to the adults after they raid the Radley's yard.

Other members of Maycomb's community portray the themes of friendship and trust throughout the novel. Sheriff Tate and some locals visit Atticus' home to warn him about the Old Sarum bunch, and Walter Cunningham's friendship with Atticus allows him to see the error in his actions. Boo also seeks to gain the children's friendship by giving them gifts in the knothole of his tree and comes to their defense when they are attacked by Bob Ewell. Harper Lee uses the character's friendship and trust towards one another to illustrate the small town, intimate setting of Maycomb.

How does Mercutio die in Romeo and Juliet?

Mercutio dies when he is stabbed by Tybalt who reaches under Romeo's arm. After this Tybalt flees with his followers.

In Act III, Scene 1, Mercutio, Benvolio, a page and servants enter a public place. Because of the heat and because the Capulets are also walking around Verona, Benvolio urges Mercutio to "retire" to their homes so that they will not become involved in a brawl. But, Mercutio, who is very short-tempered on this hot day, accuses Benvolio of getting angry at almost nothing when he is in a mood to be angry, so he should not criticize any one else.

This argument between friends sets a threatening tone for the scene. Then, as Benvolio and Mercutio quarrel, Tybalt enters with some other men. He asks to have a word with Benvolio and Mercutio. Annoyed by Tybalt's intrusion, Mercutio taunts him with puns until Romeo enters. Tybalt then turns his attention to Romeo, calling him "a villain," but since Romeo has married Juliet and is now related by marriage, he speaks kindly to Tybalt, saying that he "tender[s]" the name Capulet and loves him.
Not knowing why Romeo says these things, Mercutio is incensed--"Oh, calm, dishonorable, vile submission!"(3.1.44), and he draws his sword. He and Tybalt exchange insults and Tybalt draws his sword, too. With the intention of ameliorating things, Romeo steps between them, urging them not to fight because the Prince has forbidden "this bandying in Verona streets" (3.1.56), but Tybalt reaches under Romeo's arm and fatally stabs Mercutio.

How is Mr. Hoodhood affected by the Vietnam War in Gary Schmidt's The Wednesday Wars? How was Holling affected? How was Heather affected?

In Gary Schmidt's The Wednesday Wars, Mr. Hoodhood is somewhat emotionally affected by the Vietnam War because he sees what terrible losses the war is leading to, but in general, Mr. Hoodhood emotionally distances himself from the war because he is an emotionally distant person, mostly concerned with being a successful businessman.

We can see how emotionally affected Mr. Hoodhood is by the war when, each night, he watches Walter Cronkite on TV reporting the latest news of the troops in Vietnam. By March, rates of casualties are even higher, and Mr. Hoodhood begins voicing his emotions. In March, 5,000 marines were trapped in the Khesanh base. They could only receive supplies from helicopters, and the helicopters were frequently shot down by the 20,000 Vietcong troops surrounding the base. The Vietcong launched 500 mortar shells per day at the troops and filled tunnels with explosives. During the news reports, Mr. Hoodhood would sometimes "shake his head and whisper, 'Five thousand boys trapped. Good Lord. Five thousand'" and reach for his wife's hand, which shows how emotional he was about the news.

As a businessman, Mr. Hoodhood is a conservative who does not oppose the decisions of the government, including decisions to go to war. His greatest desire is to be elected the Chamber of Commerce Businessman of 1967. Because he wants the title, he warns his liberal daughter, who is becoming increasingly involved in the hippie movement, not to do anything foolish to prevent him from receiving the honor.

It is not an honor that is awarded to a man who has a daughter who calls herself a flower child. So go wash your face ("October").

While he finds the war emotionally distressing, Mr. Hoodhood generally refuses to become emotionally involved in the war because his priority is his work.

What led the United States to build its military forces after winning a successful war? Were the Soviets afraid of Americans as much as Americans...

After World War II, the U.S. was convinced that it had to build up its military forces to combat the growing threat from the Soviet Union. Even during the end of World War II, the Soviets had stopped their attack on Warsaw, Poland, which was then controlled by Nazis, to defeat anti-Communist forces in Poland. The U.S. had detonated two atomic bombs in Hiroshima and Nagasaki, Japan, in August of 1945 in an attempt, some historians believe, to frighten Soviets at the beginning of the Cold War. Therefore, the origins of the Cold War lie within the end of World War II. According to historian David Trowbridge, author of U.S. History, Volume 2, "both nations came to view the other as aggressive and committed to global domination by the early 1950s." Therefore, there is research that suggests that the Soviets were just as afraid of American aggression, in part resulting from the detonation of the atomic bombs, as Americans were afraid of Soviets. 

I'm not sure which documents you are referring to in the question, but the American Cold War policy was guided by documents such as NSC-68, written in 1950 by the National Security Council. This document stated that the Soviets wanted “to impose its absolute authority over the rest of the world.” NSC-68 established an aggressive approach to fighting communism. These types of approaches would likely not be successful in fighting current or recent threats, such as al-Queda, because terrorist groups are not a conventional enemy. It is therefore difficult to know how to oppose their expansion. 

What role does technology play in archaeology and history?

When we think of archaeology we may think of adventure, Indiana Jones, and hired help painstakingly brushing away dust and dirt from the precious relics of times past.  This is not the case for the modern archaeologist, though adventure is still part of the thrill.  Modern technology has allowed archaeologists to use advanced excavation techniques, enabling greater recovery of fragile artifacts.  Using technology that ranges from lidar to x-ray guns, archaeologists can view sites without disturbing the soil and the objects beneath.  This allows for greater care and planning so that archaeologists can evaluate the layout of the excavation site to allow for maximum preservation of the artifacts, skeletons, and structures.  It also allows for preventing unnecessary excavation, preserving the surrounding landscape of the site.  Using advanced techniques, we have been able to peer deeper into the past than ever before.  A perfect example of this would be the study of the condition of the teeth and bones of ancient people through the eyes of modern dentistry and medicine.  Using their remains, we gain an insight into the health, diet, lifestyle, and cause of death of the subject.  As medical science advances, every bone that is recovered tells a piece of their story.

Why does W. B. Yeats use an ambivalent tone and attitude in his treatment of the political uprising in his poem "Easter, 1916"?

"Easter, 1916" is a poem in which Yeats expresses his feelings about the Irish uprising against British rule led by reactionaries he knew personally. The poet or speaker is trying to come to terms with both the revolutionaries' violence and subsequent executions by the British government. The poem's speaker struggles between his distaste for violence in general and his admiration for the ultimate sacrifice made by these rebels. Several lines in the poem are ambiguous in nature and serve to express these conflicted feelings. The first is "A terrible beauty is born." This line is mentioned at the end of the first, second, and final stanza. This line is preceded in each case with a mention of change

All changed, changed utterly

The first stanza describes the ordinary lives of the rebels and the poet's casual encounters with them before the uprising. He would often pass them with "a nod of the head" or an exchange of "polite meaningless words." Now, all this is changed. In what way and for better or worse, the poet does not say. He just knows a "terrible beauty" is born. This oxymoron reflects the poet's ambivalent tone, as the speaker seems to fear and admire the transformation of "meaningless words" to action.  

The second stanza contributes even more to this ambivalence, as the speaker compares the rebels to stones that remain steadfast in their cause in the midst of a world that seems to be vacillating or changing "minute by minute." The speaker cannot resolve for us whether this steadfastness is good or bad, but it does set the uprising's leaders apart from the world in which they live.  

The last stanza refers to the sacrifices made by these rebels. Is it enough to "know they dreamed and are dead"? Were they excessive in their love for a cause? Were their deaths "needless"? The poet will not say, but he does go on to name each of these reactionaries—MacDonagh, MacBride, Connolly, and Pearse, acknowledging with respect that their "excess of love" for their country led to their deaths, but questioning whether their sacrifices were necessary. Did these revolutionaries inspire others with their deaths? Will more "needless deaths" occur as a result? The impact of the uprising and the resulting executions has yet to be determined. Perhaps all that can be claimed at this point is the ambivalent declaration that the Irish people ("whenever green is worn") have "changed, changed utterly." 

I included some links below that provide a deeper and more thorough understanding of the events that led to the emotions expressed in the poem.  

The product of two numbers X and Y is 3 less than the sum of the numbers. How many such integer pairs of X and Y are possible.

First we need to write the problem in mathematical language i.e. we need to write an equation.

Product of two numbers `xy,` sum of two numbers `x+y` and since the product is less by 3, we have

`xy=x+y-3`

Write `y` in terms of `x.`

`xy-y=x-3`

Factor the left side.

`y(x-1)=x-3`

Check whether `x=1` gives an integer solution.

`0=-2` 

`x=1` does not gives us an integer solution so we can assume that `x ne1` which allows us to divide by `x-1.`

`y=(x-3)/(x-1)`

Now we know that in order to get an integer solution `x-3`  must be divisible by `x-1,`  bearing in mind that `x` is an integer as well. The only thing remaining to do is to check whether those two numbers are divisible for some values of `x.`  We will start with values of `x` such that `x-1=-1` or `x-1=1` because those are certainly integers.

`x=0`

`y=(-3)/(-1)=3`

`x=-1`

`y=(-4)/(-2)=2`

`x=-2`

`y=(-5)/(-3)!inZZ`

`x=-2` is not a solution. If we keep trying with the smaller and smaller numbers we will get fractions that get closer and closer to 1, but we will never get an integer.

Let us try greater numbers. We already know that `x=1` is not a solution so we will skip that.

`x=2`

`y=-1/1=-1`

`x=3`

`y=0/2=0`

`x=4`

`y=1/3!inZZ`

Again, we see that `x=4` is not a solution and nor is any integer greater that 4.

We can conclude there are 4 such integer pair numbers and they are

`(-1,2), (0,3), (2,-1)` and `(3,0).`