Resoudre pb linear algebra

Consider the 2x2 orthogonal matrices F= [- c s ], J = [ c s ] [ s c ] [- s c ] where s=sin teta and c= cos teta for some teta. The first matrix has detF = -1 and is a reflector - the special case of a householder reflector in dimension 2. The second has det J1 and effect a rotation instead of a reflection. Such a matrix is called a givens rotation a) describe exactly what geometric effects left multiplications by F and J have on the plane IR2 ( rotates the plane by the angle teta , for example but the rotation clockwise or counter clockwise b) describe an algorithm for QR factorization that is analogous to aloritm but based on givens rotations instead of householder reflection c) show that your algorithm involves six flops per entry operated on rather than four, so that the asymptotic operation count 50% greater