Why does the King send Hamlet to England? And why does the King send Rosencrantz and Guildenstern to accompany him?
In Shakespeare's Hamlet, Ros. and Guil. are used by Claudius first, and then by Hamlet. The themes of seeming, reality and illusion are furthered by the two whose names seem interchangeable and are earlier sent by Claudius to spy on Hamlet. Claudius considers them friends of Hamlet, so it is natural that he sends them with Hamlet to England.
They are, of course, carrying the letter that will order the execution of Hamlet. Hamlet sees through this deception just as he sees through all of the other deceptions Claudius attempts, and in the end Ros. and Guil. are executed instead.
This seems a nasty fate for the two, who bear Hamlet no malice. But they have betrayed him, and this is the price they pay.
The incident establishes Claudius more concretely as a killer. By sending Hamlet to England to be assassinated, he is seen as having mounted a direct attack on Hamlet.
The king sends all of these men to England as a ploy. Supposedly, Hamlet is being sent to England to collect some tribute that is owed to Denmark.
The only reason Claudius is sending Hamlet, really, is to get rid of him. The two men with the long, hard to type names are only going to England so that they can carry a letter for King Claudius. The letter is giving an order that Hamlet should be killed. Hamlet is just being sent to England so he can be killed and Claudius won't have to worry about him anymore.
He sends him because he starts to feel that Hamlet knows that he killed his father, so, he thought if he sent him to England he'll get rid off him forever. He sent them to kill Hamlet!