Final answer:
Hamlet quickly infers that Rosencrantz and Guildenstern are sent to spy on him due to their dubious actions and vague responses, reflecting the theme of espionage in the play.
Step-by-step explanation:
Hamlet's suspicions about Rosencrantz and Guildenstern are based on their sudden appearance at Elsinore and their evasive behavior when he questions them. He quickly infers that they have been sent by King Claudius to spy on him. Rosencrantz and Guildenstern react by attempting to reassure Hamlet of their loyalty, but their answers are circuitous and fail to convince him. This concept of espionage mirrors Elizabethan concerns about surveillance and reflects the larger themes of betrayal and deceit in Shakespeare's Hamlet.