<prompt> Kokotoa anzapmatrix sqrt3 -1 1 sqrt3 endpmatrix6.  <response>: Tunaona hiloanzapmatrix sqrt3 -1 1 sqrt3 mwishopmatrix 2 anzapmatrix sqrt32 -12 12 sqrt32 mwishopmatrix 2 anzapmatrix cos fracpi6 -sin fracpi6 sin fracpi6 cos fracpi6 endpmatrix.Kumbuka kwamba beginpmatrix cos fracpi6 -sin fracpi6 sin fracpi6 cos fracpi6 endpmatrix inalingana na mzunguko wa fracpi6 karibu na asili.Kwa ujumla, kwa matrix ya kuzunguka,anzapmmatrixcostheta -sinthetasintheta costhetamwishopmatrixk anzapmatrix cos ktheta -sin ktheta sin ktheta cos kthetamwishopmmatrix.Kwa hiyo,anzapmatrix sqrt3 -1 1 sqrt3 mwishopmatrix6 26 anzapmatrix cos fracpi6 -sin fracpi6 sin fracpi6 cos fracpi6 endpmatrix6 26 anza pmatrix cos pi -sin pi sin pi cos piendpmatrix beginpmatrix -64 0 0 -64 mwishopmatrix . 