What is ironic about the toast of Montresor in "The Cask of Amontillado"?

The toast that Fortunato and Montresor share is as follows:

“I drink,” [Fortunato] said, “to the buried that repose around us.”

“And I to your long life.”

Fortunato's toast is ironic because he will soon be among the dead buried in the catacombs himself. Montresor seems to be wishing his companion a long life as a typical toast suggests, full of heath and happiness, but Montresor hopes that Fortunato will live a long time chained to wall and suffer before he dies in payment for the "insult" he dealt to Montresor. His response, therefore, is ironic as well.

What happened in Chapter 5 of Lyddie?

Lyddie has been working hard at Cutler's tavern, and I mean really hard.  Mrs. Cutler is a serious task master, and Lyddie can barely catch a moment to herself.  Fortunately, Lyddie is a hard worker, and that earns her the respect and friendship of Triphena.  That's helpful to Lyddie in Chapter Five, because in this chapter Mrs. Cutler decided to go to Boston to sell the maple sugar and visit some family.  Because of the reduced workload (Mrs. Cutler isn't there anymore), Triphena encourages Lyddie to go visit her family as well.  

Lyddie first goes to see Charlie at the mill, but she is surprised that she can't find him there.  The reason is that Charlie is still in school, which upsets Lyddie.  She's being worked to the ground, and Charlie's family is allowing him to go to school. Lyddie is disgusted at the situation and slightly worried that Charlie will forget his real family.  

The next place that Lyddie decides to visit is their former farm.  To her surprise she finds a runaway slave in the house.  This is a new experience for Lyddie for two reasons.  One, she has never seen a runaway slave before and thoughts of the reward money do creep into her head.  Two, Lyddie has never seen a black man before.  

What are some allusions in Anthem?

Another allusion in the novel Anthem is seen with Liberty, the girl Equality finds in the woods upon his escape from the society. He first meets Liberty as she is spreading seeds in a field while he is sweeping a nearby street. Their eyes lock, and they instantly fall in love. Equality takes Liberty with him to set up a new society, and he renames her Gaea. Gaea was a Greek goddess who represented Mother Earth. This shows a direct connection between Liberty's job of planting seeds and Mother Earth. Gaea also created the universe and gave birth to the first humans. It's important to note that Gaea is pregnant early on in this new society. She will be the one to start the new society as the first mother.

The new society Equality and Liberty form is an allusion to a democracy where individual rights are cherished and preserved by the people. 

The entire novel alludes to a time in the past where society is more advanced with cars, electricity, etc.  A Great War is mentioned and The Great Burning is an event where all books and knowledge is destroyed. Although there is no real reference to an actual event, Ayn Rand is trying to make us understand what could happen if we lived in a "collective," communistic society.  

If you lower the temperature enough, can all the elements be turned into solids?

Most substances found in nature exhibit a behavior where they change from solid to liquid and from liquid to gas as the temperature is raised. On decreasing the temperature the change in state is reversed.

In addition to temperature, pressure also plays a large role in what state a substance exists at. At atmospheric pressure it is possible to cool down all elements so that they are at solid state. For the element helium, in addition to an extremely low temperature (below 1.5 K) it is also required to increase pressure to above 2.5 MPa so that it changes state to solid.

It is not possible to convert all elements to the solid state merely by lowering temperature; for some elements it is important to apply an appropriately high pressure.

In The Great Gatsby, where does Nick, the narrator, come from and why?

Like Jay Gatsby and like F. Scott Fitzgerald himself, Nick Carraway comes from the Midwest (Minnesota). He describes his background in his introduction as part of Chapter 1. 

"My family have been prominent, well-to-do people in this Middle Western city for three generations."

The significance of Nick's Midwestern background are two-fold. His origins make him an outsider to the social circles covered in the New York Times society pages, the glitzy and glamorous wealthy, eastern elite. Although Nick comes from an old family with some money, he is not from a family like Tom Buchanan's, which is true "old money." 

Secondly, Nick's origin ties him to Jay Gatsby (and to F. Scott Fitzgerald as well). Gatsby goes east from the Midwest and Nick does too. In the end, neither of them succeeds in making a life there and neither of them seems to really belong. Notably, both Nick and Gatsby are reflections of Fitzgerald's biography and both seem to mirror Fitzgerald's reputed worries about "making good" and proving himself in such a way as to secure a permanent stature as one of the American elite. 

Looking more directly at the text, we should not overlook the fact that Nick sympathizes with Gatsby in the end and, throughout the story, Nick is as much of an outsider/visitor at Gatsby's parties as Gatsby is. They each desire a woman and, perhaps, a place in the high society of the east, but they end up alone. 

Is this connection explained entirely by the similar geographic backgrounds of these two characters? No, it isn't. But the fact that Gatsby and Nick Carraway each come from a more humble background than the likes Tom Buchanan serves to underscore the ultimate intimacy of these two characters - in terms of their respective stories and their positions as arrivistes on the scene, visitors to the party, as it were.

Why did Tituba finally confess to talking to the Devil in Miller's "The Crucible"?

Tituba finally "confesses" to talking to the devil at the end of Act 1 after she is repeatedly accused of doing so.  She is subjected to a barrage of questions by Rev. Hale and Mr. Parris.  She finally confesses because perhaps she realized that to confess would save her life.  She is uneducated and superstitious, so maybe it was out of fear for her life.  Mr. Parris tells her that if she doesn't confess, he will whip her to death. then Putnam immediately says that Tituba must be hanged.  It's at that point that Tituba says, "No, no, don't hang Tituba! I tell him I don't desire to work for him, sir!"  Quite likely, she realizes that if she is going to save her own life, she has to say she spoke with the devil.  She has to go along with their accusations, but at the same time, indicate that she no longer listens to the devil and that she has tried to avoid doing the evil that the devil has tempted her with.  She tells Mr. Parris that the devil has told her many times to kill him, but she has not done so.  By making herself look as virtuous as possible, she is getting herself out of what appeared to be a hopeless situation.

In "Death of a Salesman," how do Charley and Ben's attitudes differ in regard to the Lowman boys' stealing? Who is being realistic?

Charley is the realistic one as Ben only appears to Willy in his illusions or dreams. Charley is the complete opposite of Ben. Charley has attained a limited degree of success within his own town whereas Ben has been highly successful in the "big city." Charley is there with the Loman family every day, living with their problems and continuing to help them financially. He is real. Ben remains almost a figment of Willy's imagination and only appears to Willy when he retreats away from reality.