




'''simple docstring'''


from math import cos, sin
def 				SCREAMING_SNAKE_CASE(      __lowercase  ) ->   list[list[float]]:
     A:		str        =		float(__lowercase  )
     return [[scaling_factor * int(x == y  ) for x in range(2  )] for y in range(2  )]
def 				SCREAMING_SNAKE_CASE(      __lowercase  ) ->   list[list[float]]:
     A    ,						A:		Optional[int]        =		cos(__lowercase  ), sin(__lowercase  )
     return [[c, -s], [s, c]]
def 				SCREAMING_SNAKE_CASE(      __lowercase  ) ->   list[list[float]]:
     A    ,						A:		Dict        =		cos(__lowercase  ), sin(__lowercase  )
     A:		List[str]        =		c * s
     return [[c * c, cs], [cs, s * s]]
def 				SCREAMING_SNAKE_CASE(      __lowercase  ) ->   list[list[float]]:
     A    ,						A:		Any        =		cos(__lowercase  ), sin(__lowercase  )
     A:		Any        =		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 				SCREAMING_SNAKE_CASE(      __lowercase		,							__lowercase		,							__lowercase  ) ->   float:
     A:		str        =		[1 / first_term]
     A:		Optional[int]        =		1 / first_term
     for _ in range(number_of_terms - 1  ):
          first_term += common_difference
          arithmetic_progression.append(__lowercase  )
     A:		int        =		[1 / step for step in arithmetic_progression]
     return sum(__lowercase  )


if __name__ == "__main__":
     import doctest

     doctest.testmod()
     print(sum_of_harmonic_progression(1 / 2, 2, 2))






