I was listening to a lecture about the expansion of the universe and found myself confused about the light we see from very distant galaxies. These galaxies are red shifted because they are moving away from us and the photons are being stretched. Does this mean that the galaxy will appear to be rotating slower than it actually is to us? If yes, is this what is meant by time dilation? Also, if the distant galaxy were to be moving towards us instead, would it appear to be rotating faster?