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In vector calculus, the curl is a vector operator that describes the infinitesimal rotation of a vector field in three-dimensional Euclidean space. At every point in the field, the curl of that point is represented by a vector. The attributes of this vector (length and direction) characterize the rotation at that point. The direction of the curl is the axis of rotation, as determined by the right-hand rule, and the magnitude of the curl is the magnitude of rotation. If the vector field represents the flow velocity of a moving fluid, then the curl is the circulation density of the fluid. A vector field whose curl is zero is called irrotational. The curl is a form of differentiation for vector fields. The corresponding form of the fundamental theorem of calculus is Stokes' theorem, which relates the surface integral of the curl of a vector field to the line integral of the vector field around the boundary curve.
The alternative terminology rotation or rotational and alternative notations rot F and ∇ × F are often used (the former especially in many European countries, the latter, using the del (or nabla) operator and the cross product, is more used in other countries) for curl F.
Unlike the gradient and divergence, curl does not generalize as simply to other dimensions; some generalizations are possible, but only in three dimensions is the geometrically defined curl of a vector field again a vector field. This is a phenomenon similar to the 3-dimensional cross product, and the connection is reflected in the notation ∇ × for the curl.
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Answer:
Time-space compression refers to the set of processes that cause the relative distances between places (i.e., as measured in terms of travel time or cost) to contract, effectively making such places grow “closer.” The idea of a “shrinking world” is not new and, in the face of rapid advances in travel, such as the jet ...
<span>Energy produced in the center of the sun
flows out through the sun's layers in different forms, including visible
light. The sun's interior generally becomes cooler and less dense as
you move away from the center. </span><span>Rising currents of hot gas in the convection zone carry energy toward the sun's surface.</span>
Answer:
sugar cane
Explanation:
prevelant crop grown in the west jndies
