"Zochreinu Le-Chayim" - Remember us for life - is one of a number of additions, which are included in the daily Amidah (silent) prayer, beginning on Rosh HaShanah. In this striking prayer, we seek to remind God that God desires life and ought to write us in the Book of Life.
With so much uncertainty in the world, there is one thing we can say with 100% certainty: our eventual death. Unetaneh Tokef reminds us of the scary, but very real fact of our mortality and vulnerability.
The leader loudly chants, "The King," in a distinct, ancient melody, as if announcing the arrival of a government official. In this prayer, God sits upon an "exalted and uplifted throne," but God is said to sit upon other types of thrones as well.
The shofar is the one consistent sound resounded throughout Jewish history to herald both the greatest news, as well as the most tragic. The Shofarot section of the Mussaf Amidah describes the many emotional encounters we've had with this special ram's horn.
Memory is a recurring theme in the Rosh HaShanah liturgy, which is why one of its four names is Yom HaZikaron, or Day of Remembrance. The Zikhronot section of the Mussaf Amidah makes a claim that God remembers us.