Idle Vibration and Automatic Transmission Roll Back

Hi All,

I have just become the owner of a 2003 Matrix XR with 23,000 miles. I have two questions (please excuse my ignorance):

1. Whenever the car is stopped (e.g. at a light), a vibration can be felt. When the car is put into neutral or park, the vibration goes away; put the car in gear and the vibration returns. This is not a "strong" vibration like something is falling apart, but it is a vibration that is rather annoying. I have read that early (e.g. 1994 and older) 4-cyl Toyotas have this issue and that it is a symptom of the 4cylinder (e.g. normal). Is this really normal? Are there other Matrix owners with this same experience?

2. I have the automatic transmission and I notice that my Matrix will roll backwards if I am stopped on an incline, while in a forward gear (e.g. drive). If I take my foot off the brake, the car will roll backwards - like a car with a manual transmission would. Is this normal behavior?

I appreciate any of your help and feedback.

Regards,

Doones