<prompt> Je! ni matrix mathbfM ambayo hufanya mabadiliko ambayo hutuma ABCD mraba hadi ABCD ni nini? Hasa, A huenda kwa A, na kadhalika.asyukubwa 200;kuagiza grafu;jozi Z0,0, A2,3, B-3,2, C-4,1, D-1,-4;Lebo f;f.pfontsize6;xaxis-1.5,1.5,Tikitif, 1.0;yaxis-0.5,2.5,Ticksf, 1.0;chora0,0--1,0--1,1--0,1--0,0,nyekundu;nukta 0,0; leboAA, 0,0, SE;nukta 1,0; leboD, 1,0, NE;nukta 1,1; leboCD, 1,1, E;nukta 0,1; leboB, 0,1, NE;chora0,0--1,1--0,2---1,1--0,0, bluu;nukta 0,2; leboC, 0,2, NE;nukta -1,1; leboB, -1,1, W;asy  <response>: Kumbuka kuwa tunazungusha ABCD kwa 45circ na kuongeza kwa sqrt 2 ilimathbf M sqrt 2anzapmatrixcos 45zingira -dhambi 45zingira sin 45circ phantom -cos 45circmwishopmatrix anzapmatrix 1 -1 1 phantom -1 mwishopmatrix.La sivyo, tunaona kuwa mathbf M beginpmatrix 1 0 endpmatrix anzapmatrix 1 1 endpmatrix na mathbf M beginpmatrix 0 1 mwishopmatrix anzapmatrix -1 1 mwishopmatrix. Tangu mathbfM kuanzapmatrix 1 0 mwishopmatrix na mathbfM beginpmatrix 0 1 endpmatrix huamua safu wima ya kwanza na ya pili ya mathbf M, mtawalia, tunajua hili ndilo jibu letu. 