


"""simple docstring"""
from math import cos, sin






def 						lowercase				(	_snake_case		: float	)	->list[list[float]]:
	"""simple docstring"""





	__snake_case      :		Optional[Any]         =							float(_snake_case	)
	return [[scaling_factor * int(x == y	) for x in range(2	)] for y in range(2	)]






def 						lowercase				(	_snake_case		: float	)	->list[list[float]]:
	"""simple docstring"""





	__snake_case      ,				__snake_case      :		Union[str, Any]         =							cos(_snake_case	), sin(_snake_case	)
	return [[c, -s], [s, c]]






def 						lowercase				(	_snake_case		: float	)	->list[list[float]]:
	"""simple docstring"""





	__snake_case      ,				__snake_case      :		str         =							cos(_snake_case	), sin(_snake_case	)
	__snake_case      :		int         =							c * s
	return [[c * c, cs], [cs, s * s]]






def 						lowercase				(	_snake_case		: float	)	->list[list[float]]:
	"""simple docstring"""





	__snake_case      ,				__snake_case      :		Union[str, Any]         =							cos(_snake_case	), sin(_snake_case	)
	__snake_case      :		Optional[int]         =							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) = }')







from __future__ import annotations


def  A			(   lowercase       ,			lowercase					)  ->    int:
		'''simple docstring'''

		UpperCamelCase      ,    UpperCamelCase            =	0, len(lowercase					) - 1
		while start_ind <= end_ind:
				if array[start_ind] == search_item:
						return start_ind
				elif array[end_ind] == search_item:
						return end_ind
				else:
						start_ind += 1
						end_ind -= 1
    # returns -1 if search_item is not found in array
		return -1


if __name__ == "__main__":
					print(double_linear_search(list(range(100)), 40))
