Let the four horizontal compass directions north, east, south, and west be represented by units vectors nhatitalic , ehatitalic , shatitalic , and whatitalic , respectively. vertically up and down are represented as uhatitalic and dhatitalic . let us also identify unit vectors that are halfway between these directions, such as (ne)^^\^ for northeast. rank the magnitudes of the following cross products from the largest to the smallest. (use only "> " or "=" symbols. do not include any parentheses around the letters or symbols.)
(a) n^^\^ cross n^^\^
(b) w^^\^ cross (ne)^^\^
(c) u^^\^ cross (ne)^^\^
(d) n^^\^ cross (nw)^^\^
(e) n^^\^ cross e^^\^

Arocket starts from rest and moves upward from the surface of the earth. for the first 10.0 s of its motion, the vertical acceleration of the rocket is given by ay = 12.80 m/s32t, where the +y-direction is upward. (a) what is the height of the rocket above the surface of the earth at t = 10.0 s? b) what is the speed of the rocket when it is 325 m above the surface of the earth?

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.

Currents in dc transmission lines can be 100 a or higher. some people are concerned that the electromagnetic fields from such lines near their homes could pose health dangers. for a line that has current 150 a and a height of 8.0 m above the ground, what magnetic field does the line produce at ground level? express your answer in teslas and as a percentage of the earth’s magnetic field, which is 0.50 g. is this value cause for worry?