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In the passive transformation (right), point P stays fixed, while the coordinate system rotates counterclockwise by an angle θ about its origin. The coordinates of P ′ after the active transformation relative to the original coordinate system are the same as the coordinates of P relative to the rotated coordinate system.
The simplest example of a coordinate system is the identification of points on a line with real numbers using the number line.In this system, an arbitrary point O (the origin) is chosen on a given line.
A lesson plan is the teacher's guide for running a particular lesson, and it includes the goal (what the students are supposed to learn), how the goal will be reached (the method, procedure) and a way of measuring how well the goal was reached (test, worksheet, homework etc.). [2]
A sphere of radius r has surface area 4πr 2.. The surface area (symbol A) of a solid object is a measure of the total area that the surface of the object occupies. [1] The mathematical definition of surface area in the presence of curved surfaces is considerably more involved than the definition of arc length of one-dimensional curves, or of the surface area for polyhedra (i.e., objects with ...
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Relational approach: uses class topics to solve everyday problems and relates the topic to current events. [21] This approach focuses on the many uses of mathematics and helps students understand why they need to know it as well as helps them to apply mathematics to real-world situations outside of the classroom.
Testing whether a differentiable map is a diffeomorphism can be made locally under some mild restrictions. This is the Hadamard-Caccioppoli theorem: [1] If , are connected open subsets of such that is simply connected, a differentiable map : is a diffeomorphism if it is proper and if the differential: is bijective (and hence a linear isomorphism) at each point in .
Flipped classroom teaching at Clintondale High School in Michigan, United States. A flipped classroom is an instructional strategy and a type of blended learning.It aims to increase student engagement and learning by having pupils complete readings at home, and work on live problem-solving during class time. [1]