

def      snake_case__							(  lowerCAmelCase_,       lowerCAmelCase_     ):





     """simple docstring"""







     if not root or root not in binary_tree_mirror_dictionary:
          return
     SCREAMING_SNAKE_CASE		,    SCREAMING_SNAKE_CASE 		=binary_tree_mirror_dictionary[root][:2]
     SCREAMING_SNAKE_CASE 		=[right_child, left_child]
     binary_tree_mirror_dict(lowerCAmelCase_,       lowerCAmelCase_     )
     binary_tree_mirror_dict(lowerCAmelCase_,       lowerCAmelCase_     )







def      snake_case__							(  lowerCAmelCase_,       lowerCAmelCase_ = 1     ):





     """simple docstring"""







     if not binary_tree:
          raise ValueError('binary tree cannot be empty'     )
     if root not in binary_tree:
          SCREAMING_SNAKE_CASE 		=F'root {root} is not present in the binary_tree'
          raise ValueError(lowerCAmelCase_     )
     SCREAMING_SNAKE_CASE 		=dict(lowerCAmelCase_     )
     binary_tree_mirror_dict(lowerCAmelCase_,       lowerCAmelCase_     )
     return binary_tree_mirror_dictionary


if __name__ == "__main__":
 _lowerCamelCase							={1: [2, 3], 2: [4, 5], 3: [6, 7], 7: [8, 9]}
 print(f'Binary tree: {binary_tree}')
 _lowerCamelCase							=binary_tree_mirror(binary_tree, 5)
 print(f'Binary tree mirror: {binary_tree_mirror_dictionary}')




from math import cos, sin







def      snake_case__							(  lowerCAmelCase_     ):





     """simple docstring"""







     SCREAMING_SNAKE_CASE 		=float(lowerCAmelCase_     )
     return [[scaling_factor * int(x == y     ) for x in range(2     )] for y in range(2     )]







def      snake_case__							(  lowerCAmelCase_     ):





     """simple docstring"""







     SCREAMING_SNAKE_CASE		,    SCREAMING_SNAKE_CASE 		=cos(lowerCAmelCase_     ), sin(lowerCAmelCase_     )
     return [[c, -s], [s, c]]







def      snake_case__							(  lowerCAmelCase_     ):





     """simple docstring"""







     SCREAMING_SNAKE_CASE		,    SCREAMING_SNAKE_CASE 		=cos(lowerCAmelCase_     ), sin(lowerCAmelCase_     )
     SCREAMING_SNAKE_CASE 		=c * s
     return [[c * c, cs], [cs, s * s]]







def      snake_case__							(  lowerCAmelCase_     ):





     """simple docstring"""







     SCREAMING_SNAKE_CASE		,    SCREAMING_SNAKE_CASE 		=cos(lowerCAmelCase_     ), sin(lowerCAmelCase_     )
     SCREAMING_SNAKE_CASE 		=c * s
     return [[2 * c - 1, 2 * cs], [2 * cs, 2 * s - 1]]


print(f'    {scaling(5) = }')
print(f'  {rotation(45) = }')
print(f'{projection(45) = }')



print(f'{reflection(45) = }')

