If `P=[[sqrt(3)/2,1/2],[-1/2,sqrt(3)/2]], A=[[1,1],[0,1]]` and `Q=PAP^T` and `X=P^TQ^(2005)P`, then `X` equal to:

If {:P=[(sqrt3/2,1/2),(-1/2,sqrt3/2)],A=[(1,1),(0,1)]:}and Q=PAP^T," then" P^TQ^2015P , is

Let A= [{:(( sqrt(3))/(2),(1)/(2) ),( -(1)/(2) ,(sqrt( 3))/( 2)) :}],B= [{:( 1,1),(0,1):}]and C = ABA^(T) , "then "A^(T) C^(3)A is equal to

If P=2+sqrt3 , Q=2-sqrt3 , then P/Q=?

If S=[((sqrt(3)-1)/(2sqrt(2)),(sqrt(3)+1)/(2sqrt(2))),(-((sqrt(3)+1)/(2sqrt(2))),(sqrt(3)-1)/(2sqrt(2)))], A=[(1,0),(-1,1)] and P=S ("adj.A") S^(T) , then find matrix S^(T) P^(10) S .

If A=[{:(1,1),(0,1):}] and B=[{:(sqrt(3)//2,1//2),(-1//2,sqrt(3)//2):}] , then ("BB"^(T)A)^(5) is equal to

If A=[{:(1,1),(0,1):}] and B=[{:(sqrt(3)//2,1//2),(-1//2,sqrt(3)//2):}] , then ("BB"^(T)A)^(5) is equal to

If P=[(lambda,0),(7,1)] and Q=[(4,0),(-7,1)] such that P^(2)=Q , then P^(3) is equal to

Let A=[[1,1],[0,1]] and P=[[cos(pi/6),sin(pi/6)],[-sin(pi/6),cos(pi/6)]] and Q=PAP^T then P^T Q^2013 P is:

If y=sin^(-1)(xsqrt(1-x)+sqrt(x)sqrt(1-x^2)) and (dy)/(dx)=1/(2sqrt(x(1-x)))+p , then p is equal to 0 (b) 1/(sqrt(1-x)) sin^(-1)sqrt(x) (d) 1/(sqrt(1-x^2))

If p(x)=x^(2)-2sqrt(2)x+1 , then p (2sqrt(2)) is equal to