IM SIU

Here's the translation of the tweet text: "05 @ Tokyu Oasis Total distance: 2200 m --- Drill, 100 x 3 Kick, 25 x 4, 12.5UW Hard Pull, 150 x 2 1 FrBa/25 2 IM75Fr75 Paddle swim, 150 x 4, 4'00", 100H50E Drill, 100 x 2 Free, 25 x 4 x 2, Relay Paddle swim, 25 x 4, 1'30", Max Drill, 100 x 2 swim, 200 x 1, Down --- via #SwimNote"

Proof: - Let \( k \in \text{Ker } T^* \). Since \( r \in \text{Im } T \), it can be expressed as \( r = Tx \), so \( \langle k, Tx \rangle = \langle T^*k, x \rangle = \langle 0, x \rangle = 0 \). Therefore, \( k \in (\text{Im } T)^\perp \). - Let \( v \in (\text{Im } T)^\perp \). Since \( \langle T^*v, T^*v \rangle = \langle v, TT^*v \rangle = 0 \), it follows that \( T^*v = 0 \), which means \( v \in \text{Ker } T^* \).

The tweet translates to: "[That shady information-filled ○M Academy is changing its name] It’s not often seen on X, but the IM A○demy, which primarily uses Instagram to send copy-paste solicitation DMs to an unspecified number of people, seems to have changed its name to 'IYOVIA' on November 5th."

The tweet translates to: "Yuna-san's Shiugnas was being bullied. I'll beat you up...!!!!"

Here's the translation of the tweet: "Taking a walk with my newly bought drone, capturing the 'colorful autumn in the forest.' I recently learned that 'Herbst' means 'autumn' and 'Wald' means 'forest.' This is in the area around Sargans in eastern Switzerland. HOVER AIR X1 PRO MAX Switzerland Colorful Autumn in the Forest youtu.be/dE0Sq05OOmQ?si…"

Here's the translation of the tweet: "Today's unrelated practice record for Ebony. Some aspiring Pirate King said, 'I'm seeing it on X, try the opening of One Piece 😂😂' Me: 'It's tooooooooo difficult!!! 😂' We Are! I'll challenge it again when I get better 🤣🤣🤣🤣🤣" (Note: "X" likely refers to a platform, possibly Twitter, which has been rebranded.)

Here's the translation of the tweet: "I have something important to share! 🔥🔥🔥🔥🔥🔥🔥🔥🔥🔥 I have finished work!!! 🔥🔥🔥🔥🔥🔥🔥🔥🔥🔥 Tomorrow is a day off for the prefecture's citizens!! Atsu Papa has a compensatory day off!! Since the whole family is off, we are heading out now! X-time is scheduled to resume as soon as I get home 🙌"

Here's the translation of the tweet: "Shihun, Minso, and of course Hidohyun, Goggles and the flute player Seyun (the best 👏🤣), I still don't know the characters of Changyeong and Siu, but Siu is in the same 99 group and is a Puek buddy, so maybe Minuk was released because he was too much of a handful?? lol Junso, I leave it to you!! lol #Puje"

Here's the translation of the tweet: "This is Paul-kun's profile from Y2Z 🐱 IG: im.paul_04 X: Jaopaul_eiei TikTok: wpaul_poa4 #Y2Z #Y2ZProfile #ABearDayEntertainment #PAUL_Y2Z #TPOP pic.x.com/4dc1HQW7AJ"

Thank you for today as well 🙏😍 The battle was intense! I truly appreciate your cooperation 🙇🙇 Thank you, X-san and the little lion cub 🦁 🩷 First time making a teru teru bozu 😍🌈 Thank you, Kita-san~ 🩷 Tomorrow, I have a battle with Imu-san 🥊!! Many people can't come, but since we're doing it, I don't want to lose and will give it my all! 👏🏼 Good night! 🌙 pic.x.com/sfrSE9H1xX

04 @ East Sports Center Total Distance: 1800 m --- Drills, 100 x 2 Pull, 100 x 4, odd Fr even iM swim, 75 x 4 x 2, 1s Fr50 Ba25 2s Fr25E 50H drills, 50 x 4 x 2, 1s '45 2s 1'30 under 35 seconds Free, 200 x 1, turn practice & cool down --- via #SwimNote

The tweet translates to: "Whenever it seems like things are finally going well, there's always some kind of setback that comes up, and it's become such a familiar pattern that I've gotten used to it (or rather, I can already guess the source and purpose). Still, I can't help but think about how things would have been if IM and X1 had been able to continue their activities at that time..."

The translation of the tweet is: "🔥🔥🔥 🔥🔥🔥 🔥🔥🔥 🔥🔥🔥 I have finished work!!! X-time has begun!! Looking forward to tonight as well!! 🍻🍻 🍻🍻 🍻🍻 🍻🍻 🍻🍻 🍻🍻"

The translation of the tweet text is: "[R-18] Taihou x Illustris | Siu #pixiv pixiv.net/artworks/11566…"

The translation of the tweet is: "Fennec fox designed by Kyohei Katsuda 35x35cm Echizen momigami I'm typing like a bot pic.x.com/N9tcrR7ga0"