Express the unit vectors in spherical polar coordinate systems in terms of the cartesian unit vectors ii) using the results of i), find the time derivatives of iii) using the above results, find an expression for the velocity vector in terms of iv) derive the expression for speed using the velocity vector from iii).

Charge is distributed along the entire x-axis with uniform density λ. how much work does the electric field of this charge distribution do on an electron that moves along the y-axis from y = a to y = b? (use the following as necessary: a, b, ε0, λ, and q for the charge on an electron.)

The space between two 15-in.-long concentric cylinders is filled with glycerin (viscosity = 8.5 × 10-3 lb·s/ft2). the inner cylinder has a radius of 1 in. and the gap width between cylinders is 0.1 in. determine (a) the torque and (b) the power required to rotate the inner cylinder at 180 rev/min. the outer cylinder is fixed. assume the velocity distribution in the gap to be linear.

Need asap which of these is an example of a hypothesis? (2 points) a. adults were not interviewed b. the investigation was time consuming c. the source of information was biased d. very few teenagers were interviewed scientists in different parts of the world have conducted experiments to find the speed of light in vacuum. if the results of the experiments are identical, they would most likely be (2 points) a.valid b. biased c. unreliable d. non-observable which of these questions can be answered using science? (2 points) a. what is the best career? b. does water exist on venus? c. should the use of automobiles be stopped? d. which is the most interesting subject to study? the models can be best used to (2 points) recreate something which is easily observed in nature prove that all atomic theories have the same meaning demonstrate the transformation of atomic theory into law represent the locations of subatomic particles in different atomic theories 22. (bws.06) scientists earlier believed that the lowest measurable temperature is the freezing point of ice. however, modern scientists believe that temperatures below the freezing point of ice can also exist. what best accounts for these different opinions? (2 points) scientists propose contradictory ideas to include all possibilities scientists come up with different hypotheses without enough evidence scientists propose different ideas to avoid repetition of scientific knowledge scientists having different interests may interpret the same data in different ways based on the graph, what is the most likely mass of an apple chosen randomly from the basket? (2 points) between 0.10 kg and 0.12 kg between 0.12 kg and 0.14 kg between 0.14 kg and 0.16 kg between 0.16 kg and 0.18 kg a scientist studies a model of a widely accepted theory about the position of planets and sun. the model would most likely the scientist to (2 points) prove that the theory would not change in the future demonstrate how the theory can be changed into a law understand facts which cannot be easily observed prove that all other facts about the universe are incorrect one scientist discovered a new theory on the evolution of the universe. what is the next step for the scientist to take? (2 points) transform the results of the theory into universal laws of nature inform the scientific community so they can verify the results call a press conference to make the discovery popular among people encourage scientists worldwide to find an appropriate application for the results the students' observations are listed below. when an iron nail is taken near the north pole (n) of the bar magnet, it is pulled towards the magnet. when an iron nail is taken near the south pole (s) of the bar magnet, it is pulled towards the magnet. the experiment was repeated by several students using different bar magnets. based on the investigations, which of these theories would the students most likely propose? (2 points) magnets attract iron nails the poles of a magnet attract all materials iron nails are attracted towards all materials iron nails have the same properties as magnets