physics question?

Lots of good answers. Looking at your own reflection, you would see yourself just as if standing still: the assemblage of you and the mirror constitutes an inertial reference frame, in which all the laws are exactly the same as in any other. However, objects which you are passing will appear to be distorted in strange ways.

One seriously sweaty face..

Just remember there is no such thing as an ABSOLUTE velocity in our universe other than "c", which only massless particles travel at. All velocities of objects with mass are only RELATIVE to other objects with mass. The fact the guy on the side flies by you at 0.99c in the other direction only means HE would look slow and squished to you. The runner and the mirror share the same inertial reference frame, so no distortions in the mirror. Even in your bathroom, you actually are flying around the sun at a relatively high velocity, which itself orbits our galaxy at relatively high velocity, which moves towards M31 etc. etc. No distortions seen there (on good hair days).

You'd see the same as if you were standing still. Special relativity is based on the idea that the speed of light is the same for all observers. If I'm in a rocket receding from you at 0.99 of the speed of light and you shine a torch in my rear window, it will leave your torch at c and proceed along my rocket at c too. This defies common sense, and it's the reason why such weird things happen at relativistic speeds.

You will see as if there is not running at 0.99C. You can not tell the difference.

AP Physics is tough. If your math grades are at least a B then I would consider taking AP Physics. It will be tough for you unless you are really strong in math.

Well, that all depends on what is illuminating you. Doppler shift will certainly shift visible light outside the range detectable by your eyes. You need to be a lot more specific about the actual conditions around the experiment.

you holding your own mirror, no matter what speed your both traveling at (with respect to something else) will change what you see.

what you see in the bathroom mirror ever morning before going to physics class will be what you see at .99c (a relative speed).

You will see yourself.

If you look in other directions, like what's behind the mirror, you'll see a 'warped image' (disformed/bend).

The theory is called relativity...

Your eyes are fixed at arms length relative to the mirror.

Wow would you be heavy though...

You would see your self in the mirror being stretched back, although in actuality your arm is still the same distance to the mirror.

www.phy.syr.edu/courses/PHY106/Slides/PPT/Lec17-Special-Relativity.pdf