A study for the weekend

The other night I witnessed a 2RvQ ending. I normally assume that the 2 rooks have an advantage over the queen (2 attackers v 1 defender is the equation). However the player with 2 rooks sometimes has to watch out for mate tricks, and this is what happened in the game in the question. A king on the wrong square allowed a mate in 1.
So to balance the scales, a little study to occupy you over the weekend. White to play and win.
A small hint, the obvious Rd7+ is well, just too obvious (Ka8!). So the challenge is to find some other tricks. (Petrov, 1963)