Find a matrix P such that PTAP orthogonally diagonalizes A. Verify that PTAP gives the proper diagonal form. (Enter each matrix in the form [[row 1], [row 2], ...], where each row is a comma-separated list. ) A = 0 −4 0 −4 0 −3 0 −3 0 (P, PTAP)

Thelime contains the point(-3,0) and parallel x-3y=3( show all work)

Set $r$ is a set of rectangles such that (1) only the grid points shown here are used as vertices, (2) all sides are vertical or horizontal and (3) no two rectangles in the set are congruent. if $r$ contains the maximum possible number of rectangles given these conditions, what fraction of the rectangles in set $r$ are squares? express your answer as a common fraction.

Maddie's rectangular kitchen has an area of 10 square yards and a length of 3 3/4 yards. how many yards wide is maddie's kitchen?