Why can't Mazda diagnose why my car vibrates at speeds over 50 mph?

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I purchased a 2015 Mazda 3i Touring that develops a vibration when driving between 55 and 70 mph. The vibration causes the driver's side view mirror to shake and is also felt in the steering wheel and seat. Second day of ownership I had to make a fast stop on a expressway and the brake pedal bounced and vibrated, the car made this horrific sound and then continued when ever I had to stop. Brought the car in, resurfaced one front rotor. Happened again and back to the dealer a week later and they replaced all 4 rotors(I guess). The vibration was addressed and said a tire was out of balance. On the way home the vibration appeared again. A week later back to the dealer. Balanced all 4 tires and also a performed a software update. A week or 2 go by and the vibration is back! Causes fatigue, and anxiety. Back to the dealer kept the car 2 1/2/ days replaced all the wheels and tires off another vehicle like mine. Vibration still there. A friend said it could be my transmission?? Purchased new in Feb 2015 it now has 4,700 miles on it. SO disappointed as I really like the car.