Our homework is corrected by the teacher
Although the teacher is doing the action, the subject of the sentence is "our homework". It also uses a form of to be (in this case it is "is"). Both of these things are what makes a passive sentence.
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Answer: a. He is distraught and unsure.
In this excerpt, Hamlet is distraught and feels desperate. He begins to wonder whether it would be better to die, as dying is only to sleep forever. He thinks this would end his heartache, and all the pain he is subject to. However, as he continues talking, he wonders if maybe the sleep of death comes with dreams, and whether those dreams might be nightmares. This worries him, and makes him more unsure as to what choice to make.