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Latin word mutare comes from Latin moveo
moveo (Latin)
(of plants) I put forth. I arouse, excite, promote, produce. I begin, commence, undertake. I disturb, shake, remove. I excite, inspire. I exert, exercise. I move, stir, set in motion. I present or offer (an oblation or gift). I trouble, concern, torment (someone).
mutare (Latin)