A Queen and a Rook together provide a lot of firepower! In fact, they are so powerful that you have to stay alert and make sure that you don't stalemate your opponent.
The technique is similar to that used with the king and two rooks, except that the queen guarantees that the opposing king cannot meaningful approach either the queen or the rook. Here is the mating pattern in practice.
The queen and rook can also combine forces to mate in an unusual and pleasing mating pattern. Check it out!