How do I backup a disk partition to a compressed file using the Linux dd command?
You can use a combination of dd and gzip or zip to peform this task.

1. Backup the disk partition using dd:

$ dd if=/dev/sdX of=/path/to/destination/mybackup.img

2. Compress the backup file using gzip or zip:

$ gzip /path/to/destination/mybackup.img

This will create a compressed archive file called mybackup.img.gz. 

Alternatively, you can use the zip command to compress the backup file:

$ zip /path/to/destination/mybackup.img

This will create a compressed archive file called mybackup.zip.
How would I unzip and restore the resulting backup file?
To unzip and restore the backup file, you can use the following steps:

If the backup file was compressed using gzip, you can use the following command to unzip it:

$ gunzip /path/to/destination/mybackup.img.gz

If the backup file was compressed using zip, you can use the following command to unzip it:

$ unzip /path/to/destination/mybackup.img.zip

After unzipping the backup file, you can restore it to the disk partition using dd:

$ dd if=/path/to/destination/mybackup.img of=/dev/sdX

where /dev/sdX is the device name of the partition you want to restore the backup to.

Important: Before restoring the backup, make sure you have the correct device name and destination path, as using the wrong device name may result in data loss.