import math

def inner(l1, l2):
	result = 0
	for i in range(len(l1)):
		result = result + l1[i]*l2[i]
	return result

def transpose(m1):
        result = []
        for i in range(len(m1[0])):
                resl = []
                for x in m1:
                        #print(x)
                        resl.append(x[i])
                        #print(resl)
                result.append(resl)
        return result

def multi(obj,m):
        tm = transpose(m)
        result = []
        for x in obj:
                resl = []
                for i in tm:
                        #print(x)
                        #print(i)
                        resl.append(inner(x,i))
                result.append(resl)
        return result                        
      
obj = [[2,2,1],[4,2,1],[2,4,1]]

def T(obj,x,y):
        L = [[1,0,0],[0,1,0],[x,y,1]]
        return multi(obj,L)

def S(obj,x,y):
        L = [[x,0,0],[0,y,0],[0,0,1]]
        return multi(obj,L)

def R(obj, theta):
        L = [[math.cos(theta), math.sin(theta), 0],[-math.sin(theta), math.cos(theta),0],[0,0,1]]
        return multi(obj,L)
     
print(T(obj,3,2))
print(S(obj,2,1/2))
print(R(obj,math.pi/2))