What literary devices are used in The Odyssey?

There are a huge number of examples of literary devices in the Odyssey, but we can only deal with a few of them here. One of the most notable features of the poem is Homer's use of epithets—adjectives or phrases that express a particular quality or attribute of a person or thing. A few examples:

Rosy-fingered dawn.
Wine-dark sea.
Bright-eyed Athena.

Such epithets were used to make each line fit the poetic meter of dactylic hexameter. (Six feet to each line.) We should always bear in mind that the Odyssey was intended to be read aloud, so it was important for it to have the right sound and rhythm.
Similes are also frequently used. These are comparisons between two different things using the words "like" or "as." For instance, "As brave as a lion," or "My love is like a red, red rose."
In The Odyssey, similes tend to be longer, stretching out over several lines. This explains why they're often called Homeric, or epic similes. Here are some examples:

I drove my weight on it from above and bored it home like a shipwright bores his beam with a shipwright's drill that men below, whipping the strap back and forth, whirl and the drill keeps twisting, never stopping—So we seized our stake with it fiery tip and bored it round and round in the giant's eye.

This is Odysseus describing how he blinded the giant cyclops Polyphemus.

. . . its crackling roots blazed and hissed—as a blacksmith plunges a glowing ax or adze in an ice-cold bath and the metal screeches steam and its temper hardens—that's the iron's strength—so the eye of Cyclops sizzled round that stake.

Odysseus is comparing the sizzling sound of Polyphemus's burning eye to that of white-hot metal being plunged into cold water.

Think of a catch that fishermen haul in to a halfmoon bay in a fine meshed net from the white caps of the sea: how all are poured out on the sand, in throes for the salt sea, twitching their cold lives away in Helios' fiery air: so lay the suitors heaped on one another.

Odysseus, along with Telemachus, has just slaughtered the suitors paying court to Penelope. He compares them to dying fish twitching on the deck of a fishing boat, lying on top of each other after they've been caught.
Dramatic irony- This is where we know something that a character in the story doesn't. Odysseus has just recently returned to Ithaca and is about to enter his palace. He is greeted by his loyal hound, Argos, lying decrepit on a pile of dung, and about to die:

"A hunter owned him—but the man is dead in some far place."

These words are spoken by Eumaeus, a loyal goatherd. He thinks that Odysseus is dead, but in actual fact he's talking to the man himself, cunningly disguised as a beggar.
Foreshadowing- This provides us with hints as to what is to come. A good example comes from the cyclops, Polyphemus, who puts a curse on Odysseus:

“Should destiny intend that he shall see his roof again among his family in his fatherland, far be that day, and dark the years between. Let him lose all companions, and return under strange sail to bitter days at home.”

This is precisely what does happen as Odysseus is forced to wander for many years before he's finally able to return home to Ithaca.
 
 

What are the main accomplishments of the Roman empire?

It could probably be debated for a long time what the most important accomplishments of the Roman Empire were, and even what constitutes "accomplishments" (many of the people conquered by Rome did not consider that an "accomplishment"). But there are certain things that Roman culture definitely did accomplish which would not be exceeded until centuries later.The first was the Empire's stability. The Roman Empire persisted for over 1000 years even at the most conservative measure---over 2000 at the broadest measure including the Eastern Roman Empire. That is astonishing, and essentially unmatched by any other civilization. Their military strength and their ability to maintain national security was exceptional. Based on the Greeks, they essentially invented modern military discipline and chain of command, and their military hegemony maintained for centuries a lasting peace across Europe called the Pax Romana. Romans also founded many cities which went on to become global megacities today, such as London. Their language, Latin, went on to be the foundation of almost every language in Western Europe.The Romans established infrastructure such as roads and aqueducts that lasted centuries---in fact, some of it still stands. They invented concrete and book binding, and made significant advances in medicine. They had a postal system and a social welfare system. Their system of law and government became the foundation of almost all modern legal systems. Much of the world as we know it today would not exist were it not for the Roman Empire, which may be why it continues to fascinate so many people millennia later.
https://www.history.com/news/10-innovations-that-built-ancient-rome

What have been the consequences of US involvement in the Vietnam War?

The United States involvement in Vietnam affected both countries, but since the war was fought on Vietnamese soil, its greatest and most traumatic effects were on the Vietnamese people.
While 58,000 American soldiers died and 304,000 were wounded, the statistics on the Vietnamese side include a whopping four million people dead or wounded. Of these, 1.3 million were civilians, including women and children. The United States dropped over 18 million gallons of herbicides containing dioxins and 14 million tons of explosives on Vietnam. The Vietnamese economy was crippled, children were orphaned, and families and communities were destroyed.
Within the United States, the Vietnam War was polarizing, leading to massive protests and political upheavals. Many of the same people advocating increased civil rights and other forms of social change also opposed the war and this led to the growth of youth culture. The practical results of these protests included an end to the draft and resulted in lowering the voting age to 18.
https://www.cnn.com/2015/06/24/opinions/deleon-vietnam-war-effects/index.html

Did Gortsby's judgement turn out to be correct?

H.H. Munro's short story "Dusk" tells of the protagonist's, Norman Gortsby, decision to help out a seemly down on his luck young man. The young man has no money and has forgotten what hotel he is staying at. At first, Norman does not believe the young man, thinking the story to be a scam. Unfortunately for Norman, the young man has seemingly proved his story after Gortsby finds a bar of soap (which the youth says he must have lost). Norman loans the young man money to get through, with the expectation the money will be paid back. After the young man walks off, an older man returns looking for the bar of soap he lost. Essentially, Norman's initial feelings were right; the young man conned him.
Therefore, in the end, Norman's judgment does turn out to be correct. He thought the young man was lying to him about the circumstances which brought him to ask a stranger (Norman) for money. Yet, as the young man's story unfolds, more and more "truths" become apparent to Norman. Unfortunately, the "truths" turn out to be coincidental lies that make the young man's story believable. Based upon the believable nature of the story, after the missing soap appears, Norman cannot help but believe the young man. The moral of the story? Trust in your initial feelings. If nothing else, Norman learned that important lesson.

Intermediate Algebra, Chapter 2, 2.7 summary exercises, Section 2.7, Problem 40

Evaluate the inequality $\displaystyle \frac{1}{2} \leq \frac{2}{3}x \leq \frac{5}{4}$. Then give the solution in interval notation.

By using the property of Absolute value, we have

$
\begin{equation}
\begin{aligned}
5 - x &< 4 && \text{and} & 5 - x &> -4\\
\\
-x &< -4 && \text{and} & -x &> - 9
&& \text{Subtract each side by } 5\\
\\
x &> 1 &&& x &< 9 && \text{Divide each side by $-1$}
\end{aligned}
\\
\text{Remember that if you divide or multiply negative numbers, the inequality symbol reverses}
\end{equation}
$

Since the inequalities are joined with $and$, find the intersection of the two solution.
The intersection is shown and is written as $(1,9)$

Discuss the approach of the American government in promoting support for American involvement in World War I among its citizens, and evaluate the impact of these policies on the activities of the American people.

The beginning of World War I for America was the beginning of modern-day propaganda. While there has always been some form of subterfuge and propaganda in drumming up support for these sorts of ventures, the American "spin" system went to work efficiently and effectively during its campaign at the beginning of World War I.
Previously, America had remained relatively neutral, deciding to stay out of conflicts with foreign interests. That was one of the main benefits of being so far separated geographically from the rest of the Western world—it was very easy to remain disengaged. However, America had already entered wartime activities in a subtle way and was making sure to show its support however it could for Britain and its allies, with supplies and resources being ferried to the European continent frequently.
When one of these ships, the Lusitania, was destroyed, Americans were sent into an uproar—not because they thought they were being attacked for wartime activities, but because they believed the Germans had attacked innocent civilians. The general public did not know about the supplies being ferried across the ocean and believed they were simply victims. After this, public outrage was incensed, and support was encouraged through pamphlets and constant reminders about the evils of the Axis Powers.

The United States had had a policy of neutrality since its inception in the late eighteenth century. Thomas Jefferson, the third president, had warned the country of the dangers of "entangling alliances" in 1801. To counter this deep-seated tradition, the US government engaged in a propaganda campaign to win support for American participation in World War I (1914–1918).
Germany and Britain attempted to interfere with each other's commerce on the high seas during WWI. Because the British fleet was the most powerful in the world, the Germans had to rely on submarines to fight back. In 1915, the Germans sank the Lusitania. Over one hundred Americans died, and former President Theodore Roosevelt asked the current President, Woodrow Wilson, to declare war. Not ready for that, Wilson protested to the Germans and prepared the country for war. Also, the US government's public blaming of Germany was an effort to change public opinion. In fact, the Lusitania was illegally carrying munitions and Americans had been warned not to sail on the ship.
Wilson won reelection in 1916 in part because he kept the US out of the war, but American neutrality ended in 1917. Wilson tried to rally public support by claiming that America and her allies were fighting for democracy. There were Uncle Sam posters encouraging enlistment; posters exhorting the public to buy war bonds were ubiquitous. Wilson secured support from women, at least in part, by promising that women would soon be able to vote.
Propaganda was spread by the Committee on Public Information. This office was run by a former newspaper reporter, George Creel. He used modern propaganda techniques and hired tens-of-thousands of speakers to travel around the nation and rally support. A propaganda film, The Beast of Berlin, was released to public acclaim. Sauerkraut became known as "liberty cabbage," and schools stopped offering courses in German.
The U.S. government insisted that American citizens support the war effort. Dissent was not tolerated, and more than one thousand people were convicted under the Sedition and Espionage Acts. Surprisingly, the US Supreme Court upheld the legality of these draconian measures after the war in two 1919 cases.

In WWI the government was able to take advantage of social groups which already existed in America at the time. The government instituted a draft for the first time since the Civil War but had the draft administered at the local level often by prosperous men of the community. This prevented the disastrous draft riots that took place during the Civil War and made the public more accepting. Also, the government took over providing information about the war. This practice had already started when Britain cut the German transatlantic cable in the early days of the war, thus ensuring that only Entente stories reached American shores. Woodrow Wilson commissioned advertising agent George Creel to enlist people to speak in favor of the war and what people could do to help America's efforts in it. The United States also used its artists such as James Montgomery Flagg to make the famous "Uncle Sam Wants You" poster for enlistment purposes. The nation told its civic groups to organize war bond drives and to encourage "pro-American" behavior by going to work in munitions factories and willingly rationing or going without such as "the Wheatless Wednesday" initiative. People were also encouraged to tattle on German-speaking neighbors in order to be wary of espionage or saboteurs. The risk of sabotage was exaggerated but there was a sharp decrease in socialist and foreign language newspapers during this time as people embraced "Americanism" in order to promote the war effort. The government also took the direct step of reviving the old Sedition Acts used by the John Adams administration and using them to imprison anyone speaking out against the war or the draft. Eugene Debs, Socialist candidate for president, was the most famous person arrested under this act.

What does Scout learn about the importance of becoming a woman from Calpurnia?

Scout learns several important life lessons from Calpurnia concerning how to become a woman. Calpurnia is a positive role model in Scout's life and raises her to be a respectful, responsible, intelligent young woman. After Scout rudely comments on Walter Cunningham Jr.'s eating habits, Calpurnia chastises her and gives Scout a lesson regarding the importance of respecting her company.
When Calpurnia takes the Finch children to First Purchase African M.E. Church for Sunday service, Scout learns that Calpurnia is one of the few literate black citizens and has the unique ability to code switch in front of different audiences. Calpurnia also challenges a prejudiced community member in the church, and the children get a unique perspective on the black community.
Later on in the novel, Calpurnia allows Scout to help serve the Maycomb ladies attending Aunt Alexandra's missionary circle. Overall, Scout learns from Calpurnia how to carry herself and behave like a respectful woman. Scout also learns that becoming a woman requires skill, intelligence, and hard work. Calpurnia is the ideal role model for Scout because she exhibits positive character traits and spends time showing Scout how to become a respectable woman.