Ah, now I understand,

~~but it shouldn't matter. Just offset the subimage: (x-354, y-354+oy) to (x+354, y+354+oy) where oy=[distance car to center]=440-250=190. Use Graphics2D.rotate(double theta, double x, double y) to do the rotation out of the center.~~Edit: no, this was too simplistic, since I didn't account the current car direction... but sqrt(250^2 + 440^2) * 2 is also wrong

The easy way would be to use a subimage where the car-position is virtually in the center of the rect to rotate, so if the position is (250,440), then the subimage at least has to be 880x880. The diagonale is then sqrt(2*880^2)=1244

If you want to optimize this you could calculate the minimal needed subimage and use an out-of-center-rotation by projecting the rotated viewport-corners to the source image coordinate system, but the math for this could get a bit more complicated...