What are some common mistakes to avoid when calculating the area of a rectangle?
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- Consider a transformation from $(u, v)$ to $(x, y)$ given by $x = g(u, v)$ and $y = h(u, v)$. How does the area of a region in the uv-plane relate to its image in the xy-plane?
- If a point is chosen uniformly at random from a rectangle of area A, what is the probability density function?
- How is the area of a rectangular region of the ocean surface related to the amount of solar energy absorbed?
- A rectangular piece of land is to be divided into three equal rectangular plots by two parallel fences. If the original piece of land is 60 meters long and 45 meters wide, what is the area of each smaller plot?
- Is a rectangle a measurable set?
- What is the concept of density in traffic flow (vehicles per unit length or area)?
- How is the area of a rectangle different from the area of a circle?
- How is Archimedes' principle related to the buoyant force acting on a submerged object, which can be related to the volume displaced (and thus indirectly to rectangular cross-sections)?
- How is the area of a rectangle used in optics?
- What is a rectangular prism or cuboid? How is its volume calculated?
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