Any orthnormal matrix can keep the curve's shape and size unchanged?

From: Fred (fzh113_at_hecky.it.northwestern.edu)
Date: 07/30/04 

Date: Fri, 30 Jul 2004 09:29:53 -0500

Dear listers,

I have a question about the rotation operation on a curve by
an orthnormal matrix.
Suppose the curve f = [x x^2 0 0 ...0] in d-dimensional space, which
actually is a 2-dimensional quadratic curve.
Let A is an arbitrary dxd orthnormal matrix.

My question is that if the rotated curve g = A*f still keep
the quadratic curve's shape and size as f although itself is in
d-dimensional space?

Thanks for your advices.

Fred

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