The feminine of "sir" is madam or, less commonly, mistress.
Explanation
"Sir" is a formal address for men. The appropriate feminine equivalent depends on context and formality.
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Madam: This is the most common and generally accepted feminine equivalent of "sir." It's a respectful title used when addressing a woman, especially in formal settings or when her name is unknown.
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Mistress: Historically, "mistress" was used as a title equivalent to "master." However, its modern usage can be problematic. While it is technically a feminine form of "sir" (in the sense of a person in a position of authority), it now carries connotations that make it unsuitable for general use as a polite form of address. It's typically reserved for specific contexts where it denotes a woman in a position of authority or control, and even then, care should be taken.
Therefore, in most scenarios, madam is the preferred and appropriate choice.