Rotate vertical video without cropping it.

I'm probably overlooking something, as it seems to me a very basic and often needed manitpulation, but I can't seem to rotate a vertically filmed clip, and at the same time shrink it so, that it fits within my widescreen project (with black bars at the sides).

If I rotate the video, it always chops off the top and the bottom, so I am left with the middle square part of the video.

Even if I scale the video and rotate it, it first rotates, and then scales, leading to a smaller square in the center of the video.

I'm trying to create a longer movie from all clips shot at a party, and some are shot vertically.