This one is no good as this is also an opning trap. Queen delivers check and pick up the rook. I guess you technicly avoided mate but you're losing the game.
At least Black gets to live another day (only checkmate ends the game, apart from resignations, disconnections and unforeseen circumstances).
But it's not really an option. You're down a rook, you may aswell just resign. And if you don't and you play another 30 moves before resigning then you are still resigning.
You never know, it might be a 10 seconds per side game and White has 0.1 seconds left by the time he makes that move...
but on the second one white can move pawn d3 and attack the knight