The increase in moment of inertia I of a uniform rod, having thermal coefficient of linear expansion

, about an axis passing through its one end and

perpendicular to its length when its temperature is

slightly increased by T .​

Let v1, v2, w be three linearly independent vectors in r 3 . that is, they do not all lie on the same plane. for each of the following (infinite) set of vectors, carefully sketch it in r 3 , and determine whether or not it is a vector space (i. e., a subspace of r 3 ). explain your reasoning

In order for the bug to fly through the air a force has to push the bug forward. identify this force. how does the bug produce

The chart shows the costs and shipping times for materials that a company needs to build a new product. which describes the best trade-off if the company needs to start building their product within the next two years? they should order the domestic materials because it is always best to choose the fastest shipping time. they should order the imported materials because it is always best to choose the lowest cost for materials. since the shipping time is longer, they should order the domestic materials because the additional cost is worth it to get the materials in time. even though the shipping time is longer, they should order the imported materials because they are less expensive and should arrive in plenty of time to build the product.