






'''simple docstring'''




from math import cos, sin

def       __lowercase		(    __lowercase ) ->		list[list[float]]:

						'''simple docstring'''


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

def       __lowercase		(    __lowercase ) ->		list[list[float]]:

						'''simple docstring'''


						_A  ,			_A      =			cos(__lowercase ), sin(__lowercase )
						return [[c, -s], [s, c]]

def       __lowercase		(    __lowercase ) ->		list[list[float]]:

						'''simple docstring'''


						_A  ,			_A      =			cos(__lowercase ), sin(__lowercase )
						_A      =			c * s
						return [[c * c, cs], [cs, s * s]]

def       __lowercase		(    __lowercase ) ->		list[list[float]]:

						'''simple docstring'''


						_A  ,			_A      =			cos(__lowercase ), sin(__lowercase )
						_A      =			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) = }""")













'''simple docstring'''




def       __lowercase		(    __lowercase ) ->		int:

      '''simple docstring'''


      _A      =			str(__lowercase ).strip()
      if not bin_string:
            raise ValueError("Empty string was passed to the function" )
      _A      =			bin_string[0] == "-"
      if is_negative:
            _A      =			bin_string[1:]
      if not all(char in "01" for char in bin_string ):
            raise ValueError("Non-binary value was passed to the function" )
      _A      =			0
      for char in bin_string:
            _A      =			2 * decimal_number + int(__lowercase )
      return -decimal_number if is_negative else decimal_number


if __name__ == "__main__":
    from doctest import testmod

    testmod()





