Here are the rewritten sentences:

1. The weather is so hot that I can’t go outside.
⇒ So hot that I can’t go outside.

2. She is such a good cook that her dishes always receive compliments.
⇒ Such a good cook that her dishes always receive compliments.

3. A dog is so well-trained that it obeys commands without hesitation.
⇒ Such a well-trained dog that it obeys commands without hesitation.

4. I was so scared that my heart felt like it was pounding out of my chest.
⇒ So scared that my heart felt like it was pounding out of my chest.

5. She studied so hard that she got the highest grade in the class.
⇒ So hard that she got the highest grade in the class.

6. The manager provides such constructive feedback that it helps employees improve.
⇒ Such constructive feedback that it helps employees improve.