

from math import cos, sin





def  _snake_case		(snake_case_					:     float  )							->		list[list[float]]:
  __UpperCAmelCase	:  Dict		=     float(snake_case_  )
  return [[scaling_factor * int(x == y  ) for x in range(2  )] for y in range(2  )]





def  _snake_case		(snake_case_					:     float  )							->		list[list[float]]:
  __UpperCAmelCase,			__UpperCAmelCase	:  Any		=     cos(snake_case_  ), sin(snake_case_  )
  return [[c, -s], [s, c]]





def  _snake_case		(snake_case_					:     float  )							->		list[list[float]]:
  __UpperCAmelCase,			__UpperCAmelCase	:  str		=     cos(snake_case_  ), sin(snake_case_  )
  __UpperCAmelCase	:  Dict		=     c * s
  return [[c * c, cs], [cs, s * s]]





def  _snake_case		(snake_case_					:     float  )							->		list[list[float]]:
  __UpperCAmelCase,			__UpperCAmelCase	:  int		=     cos(snake_case_  ), sin(snake_case_  )
  __UpperCAmelCase	:  List[Any]		=     c * s
  return [[2 * c - 1, 2 * cs], [2 * cs, 2 * s - 1]]


print(F'''    {scaling(5) = }''')
print(F'''  {rotation(4_5) = }''')
print(F'''{projection(4_5) = }''')







print(F'''{reflection(4_5) = }''')







'''simple docstring'''







def 				_snake_case (		lowercase						)       ->       int:
				if not isinstance(lowercase			,    lowercase						):
								__a       :     Union[str, Any]								=	F"""Input value of [number={number}] must be an integer"""
								raise TypeError(lowercase						)
				if number < 1:
								raise ValueError("""Input must be a positive integer"""						)
				return number * (2 * number - 1)


if __name__ == "__main__":
					import doctest

					doctest.testmod()