Yes - under FRAP 4(a)(4) IF the motion is one under FRCP 52(b), 59 or 60 (special rules apply re 60). Note that there is technically not a "thing" called a motion for reconsideration in the federal rules (unless you have a special case under Florida Local Rules). The motions listed above have much more technical and restrictive requirements than simply asking to reconsider.
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Only if it is timely.
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