  Rotors were introduced in Graph Theory by W.Tutte. The concept was adapted to
Knot Theory as a generalization of mutation by Anstee, Przytycki and Rolfsen in
1987. In this paper we show that Tristram-Levine signature is preserved by
orientation-preserving rotations. Moreover, we show that any link invariant
obtained from the characteristic polynomial of Goeritz matrix, including
Murasugi signature, is not changed by rotations. In 2001, P. Traczyk showed
that the Conway polynomials of any pair of orientation-preserving rotants
coincide. But it was still an open problem if an orientation-reversing rotation
preserves Conway polynomial. We show that there is a pair of
orientation-reversing rotants with different Conway polynomials. This provides
a negative solution to the problem.
