If I have a rectangle 2inches long and 4 inches wide and I rotate the rectangle 45 degrees will the length still be 2 inches?

I think that those of us who teach mathematics sometime make it seem far removed from the physical world we live in. It is not. Take a piece of paper and cut a rectangle that is 4 inches by 2 inches. Lie it on the table and then rotate it and way you like. The dimensions of the piece of paper are still the same. It is 4 inches by 2 inches. Which you call the length and which the width is up to you. Most of the time we refer to the longer dimension as the length but there is no reason you must do so.