Describe the geometric meaning of the following mappings in cylindrical coordinates. (a) (r, θ, z) ↦ (r, θ, −z) There is a reflection across the xz plane. There is a reflection across the yz plane. There is a reflection across the xy plane. There is a rotation by π about the z-axis. There is a rotation by π about the y-axis. (b) (r, θ, z) ↦ (r, θ + π, −z) There is a reflection across the yz plane with a rotation by −π about the z-axis. There is a reflection across the xy plane with a rotation by −π about the y-axis. There is a reflection across the yz plane with a rotation by π about the y-axis. There is a reflection across the xz plane with a rotation by π about the z-axis. There is a reflection across the xy plane with a rotation by π about the z-axis. (c) (r, θ, z) ↦ −r, θ − π 4 , z There is a rotation by − 5π 4 about the x-axis. There is a reflection across the yz plane with a rotation by − 5π 4 about the z-axis. There is a rotation by − 5π 4 about the z-axis. There is a reflection across the yz plane with a rotation by − 5π 4 about the x-axis. There is a reflection across the xy plane with a rotation by − 5π 4 about the z-axis.

You have been consulted by the mobile phone company hookup about a new augmented reality product called “brows”. they want to develop an alternative to google glasses, which, you recall, is a proposed new product which plans to superimpose a whole range of wireless google services over the user’s ordinary vision of the world. these appear in little circles and ovals, and let you phone people, take photographs, navigate across cities and inside buildings, find shops and update your social media. brows would do this too, but not be limited to special google services. the user would wear a small cylinder-shaped device designed to fit on top of their existing eyewear (glasses or sunglasses). it would project a reversed image onto the inside of the lenses, the reflection of which would be in focus for the user. instead of voice control, the user would control the device by eye and neck movements, which the device would track. the device would connect via bluetooth to the user’s phone, which would supply most of the computing power and wireless connectivity. hookup also wants to know what existing services would be most in demand, and which would not work well with brows. using your knowledge of augmented reality, wearable technology and interface design, is the project feasible? if not, why not? if feasible, how could the product need to be modified for a better experience?

How is coal extracted from mountaintop removal mines? a. dynamite is used to create underground tunnels where miners go to extract the coal. b. dynamite is used to break apart rocks and then draglines are used to remove the broken rock and reach the coal. c. coal in mountaintops is extracted by digging strips in the landscape to reach the coal. d. placer deposits in mountain river bottoms are removed by

Madison pushes with a 210-n horizontal force on a 24-kg crate of coffee resting on a warehouse floor. the force of friction on the crate is 74 n. what is the acceleration?