1. What is Claudius' main fear in the immediate aftermath of Polonius' death?
He could have been killed (or he will be next). And that he will be blamed for Polonius's death because he couldn't keep Hamlet under control.
Act IV, Scene 2
1. What does Hamlet refuse to tell Rosencrantz and Guildenstern?
The whereabouts of Polonius's dead body.
Act IV, Scene 3
1. What image does Hamlet use (ll. 19-29) to warn Claudius he's only king temporarily?
A man may fish with a worm that ate a king and then eat the fish that he catches with said worm. Which may mean that Claudius can be replaced quickly.
2. Claudius ends the scene by writing a letter: to whom, and what order does it contain?
He writes to the English King and plans to have Hamlet killed when he reaches England.
Act IV, Scene 4
1. What's the value of the land Fortinbras' army is marching to capture in Poland (l. 20)? What will the invasion itself cost (l. 25)?
Land = 20,000 ducats (The Captain wouldn't pay over 5 ducats though)
Invasion - 2,000 men & 20,000 ducats
2. Hamlet's soliloquy (ll. 32-66) is self-critical; summarize his main fault.
He is afraid of taking action. His cowardly hesitation is holding him back. You don't need a good reason too fight if your honor is at stake. He admires Fortinbras's will to fight for his honor.
Act IV, Scene 5
1. Ophelia's songs during her first appearance in this scene deal with love, death and sex. Why? What do they tell us about her at the moment? What might they reveal about Her, Hamlet and Polonius?
Her songs after Claudius enters are strange because they hint that Hamlet took Ophelia's virginity and refused to marry her because she was not longer 'pure' (Hamlet tricked her into bed by making a promise to marry her but won't marry her). She has gone crazy and there are two probable reasons: her father died, and Hamlet, the love of her life left her during her time of need.
2. Why is Laertes a danger to Claudius' throne (ll. 98-103)? (Actually two or three related reasons.)
~ Laertes has a large group of followers that want him to be King
~
3. What does Claudius offer as assurance that he had no part in Polonius' death (ll. 190-9)?
He tells Laertes to find his most trusted friend to hear both sides of the story and decide who is telling the truth. If Claudius isn't, he will hand over his kingdom, crown, life and everything he owns to Laertes.
Act IV, Scene 6
1. Horatio receives a letter from Hamlet explaining how he escaped from Rosencrantz and Guildenstern. How did he?
He was captured by pirates! Their ship was attacked but Hamlet talks to the pirates and ends up being the only one taken captive by these friendly buccaneers.
Act IV, Scene 7
1. What reason does Claudius give Laertes for Hamlet's killing of Polonius (ll. 1-4)?
Hamlet was trying to kill Claudius instead of Polonius
2. What are his two reasons for not charging Hamlet with murder (ll. 9-24)?
~ The Queen loves Hamlet very much and she is part of his life so he doesn't want to offend/upset her
~ The public also loves and respects Hamlet
So by punishing Hamlet, it would make Gertrude and the public hate Claudius
3. Claudius reveals that Laertes is famous for his skill with the rapier (a fencing weapon) and that Hamlet is envious of this fame.
Good for Laertes? =)
4. How does Claudius plan to exploit this envy to give Laertes a chance for (publicly) guiltless revenge (ll. 126-38)?
Have a fencing competition!! He thinks that Hamlet will never be able to beat Laertes! Hamlet and Laertes will fence in a duel, but Laertes will actually have a sharpened sword.
5. How does Laertes refine the plan (ll. 138-147)?
Not only will he have a sharp sword in their duel, he will dip his sword in poison. Claudius says he will put poison in a glass of wine for Hamlet so they will kill him one way or another.
6. What announcement does Gertrude make to end Act IV?
Ophelia has drowned. =(