The battery of my Cobalt died, the speedometer.

It sounds like it just jumped from the surge when the new battery was connected. Since it is run with a "stepper" motor instead of a cable, the pointer is positioned electromagnetically and it just looks for the shortest distance from where it is to where it wants to be. That can make it turn the wrong way and get stuck under the locating peg at "0", or it can end up exactly backward from where it should be. If the speedometer has a stop peg at "0", drive more than half the maximum speed of the speedometer. When the shortest way to that speed is counter-clockwise, the pointer will go there, then follow the car's speed down like normal. On some cars you can remove the plastic cover and push the pointer back to where it should be. Your mechanic can also use their scanner to run the gauge test sequence. That will run all the gauges up in increments, then back down to synchronize them.