code: 
  
  
  from math import cos, sin
  
  
  
  
  
  
  def 		_A		(		_lowercase   )				->   list[list[float]]:
  
  
       """simple docstring"""
  
  
       __UpperCamelCase   = float(_lowercase   )
       return [[scaling_factor * int(x == y   ) for x in range(2   )] for y in range(2   )]
  
  
  
  
  
  
  def 		_A		(		_lowercase   )				->   list[list[float]]:
  
  
       """simple docstring"""
  
  
       __UpperCamelCase,						__UpperCamelCase   = cos(_lowercase   ), sin(_lowercase   )
       return [[c, -s], [s, c]]
  
  
  
  
  
  
  def 		_A		(		_lowercase   )				->   list[list[float]]:
  
  
       """simple docstring"""
  
  
       __UpperCamelCase,						__UpperCamelCase   = cos(_lowercase   ), sin(_lowercase   )
       __UpperCamelCase   = c * s
       return [[c * c, cs], [cs, s * s]]
  
  
  
  
  
  
  def 		_A		(		_lowercase   )				->   list[list[float]]:
  
  
       """simple docstring"""
  
  
       __UpperCamelCase,						__UpperCamelCase   = cos(_lowercase   ), sin(_lowercase   )
       __UpperCamelCase   = 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) = }""")
  
  
  
style_context: 
  
  
  def 		_A		(		_lowercase   )				->   bool:
  
  
       """simple docstring"""
  
  
       if not isinstance(_lowercase				,     _lowercase   ):
            raise ValueError('Input series is not valid, valid series - [1, 2/3, 2]'   )
       if len(_lowercase   ) == 0:
            raise ValueError('Input list must be a non empty list'   )
       if len(_lowercase   ) == 1 and series[0] != 0:
            return True
       __UpperCamelCase   = []
       __UpperCamelCase   = len(_lowercase   )
       for i in range(0				,     _lowercase   ):
            if series[i] == 0:
                 raise ValueError('Input series cannot have 0 as an element'   )
            rec_series.append(1 / series[i]   )
       __UpperCamelCase   = rec_series[1] - rec_series[0]
       for index in range(2				,     _lowercase   ):
            if rec_series[index] - rec_series[index - 1] != common_diff:
                 return False
       return True
  
  
  
  
  
  
  def 		_A		(		_lowercase   )				->   float:
  
  
       """simple docstring"""
  
  
       if not isinstance(_lowercase				,     _lowercase   ):
            raise ValueError('Input series is not valid, valid series - [2, 4, 6]'   )
       if len(_lowercase   ) == 0:
            raise ValueError('Input list must be a non empty list'   )
       __UpperCamelCase   = 0
       for val in series:
            answer += 1 / val
       return len(_lowercase   ) / answer
  
  
  if __name__ == "__main__":
      import doctest
  
      doctest.testmod()
  
  
  