JPEG is a lossy compression scheme, so decompression-manipulation-recompression normally reduces the image quality further for each step. Is it possible to rotate a
Unless you rotate by multiples of 90 degrees then your image will have to perform some kind of interpolation which might reduce the quality of your image. Using a good interpolation algorithm will help here.
As for opening and recompressing, I am not sure you would actually get worse quality, but then I am not sure exactly how JPEG works.
I suggest you try to compress, manipulate and recompress and see for yourself if the result is good enough. What is good enough is subject to your application.