2006 V6 rough idle on cold start and slow shifts 1st to 2nd

My week-old, 370-miles 2006 V6 GLS is having a couple of issues.

First is a rough idle when first started. Starts right up, RPM runs up
to about 1250 and there is some seat-shaking shuddering and vibration.
It smooths out after about 30 seconds or so and the idle speed drops
closer to 1000.

Put it into drive and there is no problem with takeoff or power. Idle
drops to around 500 with the car stopped and still in gear. No
vibration.

It doesn't seem to do this if the car is started warm but I need to
double-check that.

The second issue is the slow shift timing between first and second
gears. The delay seems about twice is long as it should be. I mean,
it actually sort of lurches like a manual as first declutches, there's
a pausepause, and then wham, second engages. It's somewhat
disconcerting when trying to make a "quick turn and accellerate move"
like turning onto a busy road. Power drops right out just as soon as
you need to avoid the dump truck doing 70 in a 35.

It seems to be worse when trying to hit the gas and turn at the same
time, versus straight line accelleration.

Any ideas or comments?

Thanks!

 

It's 2006 Sonata V6. My bad. Would help to put the name in there.
doh.

 

trip to dealer.

 

If you live in Calif, 3 trips to the dealer and you get a new car!!!