<prompt> Mzunguko unaozingatia asili huchukua beginpmatrix 13 0 endpmatrix hadi beginpmatrix 5 -12 endpmatrix. Mzunguko huchukua vekta gani anzapmatrix 0 1 mwishopmatrix hadi?  <response>: Tumbo la mzunguko lazima liwe la umbo beginpmatrix cos theta -sin theta sin theta cos theta endpmatrix. Hivyo,anzapmatrix cos theta -sin theta dhambi theta cos theta mwishopmatrix anzapmatrix 13 0 mwishopmatrix anza pmatrix 5 -12 endpmatrix.Hii inatupa cos theta frac513 na sin theta -frac1213 . Kwa hivyo, beginpmatrix 0 1 endpmatrix inachukuliwa hadianzapmatrix frac513 frac1213 -frac1213 frac513 endpmatrix startpmatrix 0 1 mwishopmatrix anzapmatrix 1213 513 mwishopmatrix. 