






'''simple docstring'''







from math import cos, sin


def 			__UpperCamelCase				(			lowercase_					:     float      ):
       """simple docstring"""




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


def 			__UpperCamelCase				(			lowercase_					:     float      ):
       """simple docstring"""




       a_    ,  a_	    = cos(lowercase_      ), sin(lowercase_      )
       return [[c, -s], [s, c]]


def 			__UpperCamelCase				(			lowercase_					:     float      ):
       """simple docstring"""




       a_    ,  a_	    = cos(lowercase_      ), sin(lowercase_      )
       a_	    = c * s
       return [[c * c, cs], [cs, s * s]]


def 			__UpperCamelCase				(			lowercase_					:     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 			__UpperCamelCase				(			lowercase_					:     int      ):
       """simple docstring"""




       if not isinstance(lowercase_      ,					lowercase_      ):
              raise ValueError('double_factorial() only accepts integral values'      )
       if num < 0:
              raise ValueError('double_factorial() not defined for negative values'      )
       a_	    = 1
       for i in range(lowercase_      ,					0      ,					-2      ):
              value *= i
       return value


if __name__ == "__main__":
  import doctest

  doctest.testmod()




