A stationary source S generates circular outgoing waves on a lake. Thewave speed is 5.0 m/s and the crest-to-crest distance is 2.0 m. A personin a motor boat heads directly toward S at 3.0 m/s. To this person, thefrequency of these waves is:

Space-time metric ds2= -dt2+at2dx2+bt2dy2+ct2dz2 (a)how does the area of a rectangle with vertices at ( x=0, y=0, z=0 ), (1,0,0 ), ( 0,1,0 ) and (1,1,0 ) changes with time? (b) if a photon moving in the x direction starts from the origin at t=1, when does it reach x=l? (ds=0 for the trajectory of a photon.) (c) the proper time for a particle is defined by cd=ds. what is the proper time for a particle to move along the trajectory ( x(t)=t, y(t)=0, z(t)=0 ) from t=0 to 1 ? what is the condition on the parameter a so that the velocity of the particle never exceeds the speed of light ?

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?

When the magnetic domains in a material can be aligned, but eventually drift out of alignment, the material is