By pinning the king along the edge of the board. You want your king on the same rank or file as the king with one space in between. Then all you have to do is get your queen in between the kings. Checkmate.
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You mean Rook and a king will it depends where your at so lets say your king is across your rook and there are other opponents on your team they all are surrounding the king and they all can kill the king and so can your rook that's one way to kill the king.