I wouldn't resign like you said, I would play g6 to stop the check.
After taking my rook if you think the game is over think again. Black can close the queen in the corner and try to get her. As white you need to play accurate moves to free your queen before I can introduce her to my other rook.
any feedback is very nice please thumbs up and subscribe. i realize the voice is kind of low.
http://www.youtube.com/watch?v=gcDJC6YBDE0